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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

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

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

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

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

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

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

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

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.25

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

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

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.66

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

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

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.02

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

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

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.03

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

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

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.75

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

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

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.49

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

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

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

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

-----------------------------------------------
CPU time used                    :  00:04:33.31

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

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

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.46

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

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

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.26

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

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

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5393
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:41.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4226
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:34.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:01.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7471
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:01.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:52.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:58.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


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

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

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

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


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

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

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

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


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

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

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

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:08.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


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

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

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

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     124
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:29.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.17
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.65
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.17
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.92
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.76
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.96
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.77
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.58
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1486.56
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6918.44
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:48.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.64
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.64
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:02.25

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

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

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

Number of degrees of freedom          :    5
Value of the statistic                :    3.10
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

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

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

Number of degrees of freedom          :  119
Value of the statistic                :   98.93
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

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

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

Number of degrees of freedom          : 5039
Value of the statistic                : 5154.37
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

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

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

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:05.07

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

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

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45739
p-value of test                       :    0.74


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

  j =  0                              :    1743165869739
  j =  1                              :        399908527
  j =  2                              :            45729
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.86

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

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

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45859
p-value of test                       :    0.54


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

  j =  0                              :    1743165869859
  j =  1                              :        399908285
  j =  2                              :            45853
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

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

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

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

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


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

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:27.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

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

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


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

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

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:17.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


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

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


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

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:59.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

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

-----------------------------------------------
CPU time used                    :  00:01:52.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:33.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    : 9.61e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

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

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    : 7.68e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Normal statistic                      :  -0.032
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:37.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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



-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:37.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.06
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.91
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.64
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   67.78
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.38
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.96
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.34
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:32.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.27
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

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

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.44
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17297.60
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



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

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.87
p-value of test                       :    0.99


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

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.62
p-value of test                       :    0.88


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

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.21
p-value of test                       :    0.45


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

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.40
p-value of test                       :    0.24


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

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.26
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



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

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.95
p-value of test                       :    0.42


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

Number of degrees of freedom          :   35
ChiSquare statistic                   :   61.81
p-value of test                       :  3.4e-3


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

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.78
p-value of test                       :    0.42


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

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.51
p-value of test                       :    0.97


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

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.95
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



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

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.31
p-value of test                       :    0.71


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

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.75
p-value of test                       :    0.15


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

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.27
p-value of test                       :    0.13


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

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.03
p-value of test                       :    0.24


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

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.33
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



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

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.88
p-value of test                       :    0.49


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

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.09
p-value of test                       :    0.62


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

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.13
p-value of test                       :    0.59


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

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.03
p-value of test                       :    0.18


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

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.26
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:48.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



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

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.09
p-value of test                       :    0.96


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

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.06
p-value of test                       :    0.23


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

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4869.51
p-value of test                       :    0.90


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

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.21
p-value of test                       :    0.76


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

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



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

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.27
p-value of test                       :    0.79


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

Number of degrees of freedom          :  384
ChiSquare statistic                   :  322.86
p-value of test                       :    0.99


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

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.12
p-value of test                       :    0.66


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

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.96
p-value of test                       :    0.63


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

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.94
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.22
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:14.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.58
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:12.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.83e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    : 7.35e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 5.54e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

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

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.01
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.25
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

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

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.72
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:11.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.38
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:11.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10176.76
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9837.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:42.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



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

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

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

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.18
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



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

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4814.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:49.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.78
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11945.57
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11957.64
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:29.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.00
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999964955

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.85
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000065200

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

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

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

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

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

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

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

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:





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

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:24.67

 All tests were passed




Server wird beendet - Lösche Semaphor 102268949.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

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

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

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

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

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

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

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

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

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

-----------------------------------------------
CPU time used                    :  00:02:49.18

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

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

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.85

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

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

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.83

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

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

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.02

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

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

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.83

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

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

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.02

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

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

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.14

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

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

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.07

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

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

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.51

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

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

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

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

-----------------------------------------------
CPU time used                    :  00:04:14.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5509
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:46.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:37.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:45.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:07.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:24.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:24.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:05.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:40.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


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

A2 test on the values of A2 (m-NP)    :    2.06
p-value of test                       :    0.09

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

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

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    4.50
p-value of test                       :  5.0e-3

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


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

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

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

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


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

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

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

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     329
p-value of test                       :    0.05

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

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:10.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


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

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

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

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:37.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.12
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.94
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.97
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.12
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.44
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.55
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.27
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.12
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:34.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1502.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:59.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6949.52
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.04
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.27
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:05.42

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

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

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

Number of degrees of freedom          :    5
Value of the statistic                :    6.84
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

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

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

Number of degrees of freedom          :  119
Value of the statistic                :  139.41
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

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

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

Number of degrees of freedom          : 5039
Value of the statistic                : 4900.76
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

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

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

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

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

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45612
p-value of test                       :    0.89


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

  j =  0                              :    1743165869612
  j =  1                              :        399908779
  j =  2                              :            45606
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.68

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

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

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


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

  j =  0                              :    1743165869769
  j =  1                              :        399908467
  j =  2                              :            45759
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


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

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:35.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


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

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:26.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


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

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

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

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:57.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

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

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


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

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

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


-----------------------------------------------
CPU time used                    :  00:02:12.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

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

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:32.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

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

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:38.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.34
p-value of test                       :    0.40

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

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.17
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.01
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.57
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.39
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.08
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.26
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:02.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

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

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

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

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.84
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17432.31
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



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

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.38
p-value of test                       :    0.05


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

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.28
p-value of test                       :    0.03


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

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.45
p-value of test                       :    0.25


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

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.64
p-value of test                       :    0.72


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

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.66
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



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

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.04
p-value of test                       :    0.56


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

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.27
p-value of test                       :    0.22


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

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.29
p-value of test                       :    0.18


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

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.81
p-value of test                       :    0.36


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

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.26
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



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

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.14
p-value of test                       :    0.41


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

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.11
p-value of test                       :    0.35


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

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.29
p-value of test                       :    0.71


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

Number of degrees of freedom          :  136
ChiSquare statistic                   :   99.40
p-value of test                       :    0.9921


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

Number of degrees of freedom          :   74
ChiSquare statistic                   :   41.24
p-value of test                       :    0.9993    *****


-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



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

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.30
p-value of test                       :    0.03


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

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.64
p-value of test                       :    0.28


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

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.03
p-value of test                       :    0.77


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

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.74
p-value of test                       :    0.40


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

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.27
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



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

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.61
p-value of test                       :    0.27


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

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.55
p-value of test                       :    0.54


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

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.39
p-value of test                       :    0.76


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

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.58
p-value of test                       :    0.82


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

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.43
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



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

Number of degrees of freedom          :  384
ChiSquare statistic                   :  317.05
p-value of test                       :    0.9946


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

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.99
p-value of test                       :    0.35


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

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.29
p-value of test                       :    0.41


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

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.94
p-value of test                       :    0.72


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

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.27
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:48.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.69
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:17.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.90
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:20.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

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

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

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

-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.53e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.88
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.27
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

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

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:10.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.44
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10203.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

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

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9723.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



-----------------------------------------------
Normal statistic                      :    2.22
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:56.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:04:02.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



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

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

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

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4993.19
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



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

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

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

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

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.68
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.76
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.16
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11583.86
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11733.62
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:29.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.34
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999935318

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.54
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000023035

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

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

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

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

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:





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

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:14:34.85
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 C (L=1000, r=0)     0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 102793237.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

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

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

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

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

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

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

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

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.02

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

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

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.51

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

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

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.45

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

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

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.85

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

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

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.76

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

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

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.30

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

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

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.42

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

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

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

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

-----------------------------------------------
CPU time used                    :  00:04:12.55

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

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

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.13

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

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

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5315
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:43.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:37.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:35.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:53.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:02.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:02.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:54.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:57.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


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

A2 test on the values of A2 (m-NP)    :    2.01
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

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

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:45.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

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


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

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

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

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

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


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

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

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

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:13.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Stat. AD on the N values (NP)         :    2.24
p-value of test                       :    0.07


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

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

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

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:39.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.64
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.66
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.90
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.81
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.31
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  485.84
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.15
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:06.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7142.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:50.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.21
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

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

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.71
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:11.92

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

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

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

Number of degrees of freedom          :    5
Value of the statistic                :    3.21
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

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

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

Number of degrees of freedom          :  119
Value of the statistic                :  142.55
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

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

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

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.22
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

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

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

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:16.21

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

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

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45817
p-value of test                       :    0.61


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

  j =  0                              :    1743165869817
  j =  1                              :        399908371
  j =  2                              :            45807
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.07

Generator state:




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

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

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

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45535
p-value of test                       :    0.95


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

  j =  0                              :    1743165869535
  j =  1                              :        399908934
  j =  2                              :            45527
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


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

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:30.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

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

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


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

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


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

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

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:46.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


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

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:59.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

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

-----------------------------------------------
CPU time used                    :  00:01:55.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

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

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.03e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    : 6.30e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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

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



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:44.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.75
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.78
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.40
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.79
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.31
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.68
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.10
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.29
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.38
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

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

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.50
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17158.63
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


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



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

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.00
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.69
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.59
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.18
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.98
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.98
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.22
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.51
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.97
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.95
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.66
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.99
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.90
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.70
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.83
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.66
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.84
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.42
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.90
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.29
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.83
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5202.81
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.35
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.14
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.92
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.49
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4879.94
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  460.29
p-value of test                       :  2.4e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.76
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.06
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:25.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.25
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -1.74
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:25.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.79
p-value of test                       :    0.04

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.08e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 2.10e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.73
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.85
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:05.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.08
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:07.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.22
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:04:20.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5015.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:53.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.54
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:55.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.16
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.83
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12076.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:32.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12154.52
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:32.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.61
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000009964

Normal statistic for number of bits   :   0.079
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.42
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999996593

Normal statistic for number of bits   :  -0.027
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:40.53

 All tests were passed




Server wird beendet - Lösche Semaphor 104038421.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1257
p-value of test                       :    0.9983

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334377
  j =  1                              :        599997486
  j =  2                              :             1257
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5363
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:50.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:38.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7124
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:36.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:54.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:02.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:03.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:55.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:02.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.16
p-value of test                       :    0.9976

Test on the Nm values of W_{n,i}(mNP1):    2.37
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    3.48
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:11.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:42.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.34
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.95
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.73
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  278.78
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.49
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.10
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:10.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7222.01
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:53.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.65
p-value of test                       :  6.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.16
p-value of test                       :  8.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   12.80
p-value of test                       :    0.9974

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.0e-3

Anderson-Darling statistic = A2       :    4.15
p-value of test                       :  7.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   90.79
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:03:08.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.35
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:37.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4807.95
p-value of test                       :    0.9901


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9968


-----------------------------------------------
CPU time used                    :  00:02:59.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45518
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869518
  j =  1                              :        399908964
  j =  2                              :            45518
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46228
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870228
  j =  1                              :        399907547
  j =  2                              :            46222
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:29.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  9.1e-3

Kolmogorov-Smirnov- statistic = D-    : 3.21e-3
p-value of test                       :    0.9965

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9932


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:18.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-3
p-value of test                       :    0.9987

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:36.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.58e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.50e-5
p-value of test                       :    0.9910

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:43.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.20
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.95
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.58
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.22
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.38
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.63
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.93
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.42
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.98
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17414.46
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.40
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.68
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.90
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.62
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.20
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.33
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.88
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.65
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.67
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.02
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.89
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.37
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.89
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   42.82
p-value of test                       :    0.9986


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.63
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.68
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.95
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.54
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.93
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.27
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.51
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4922.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.13
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.66
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.13
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.78
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.86
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.64
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.80
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.76
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.30
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    1.63
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:24.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 3.79e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.94
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.47
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.00
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:12.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:15.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10311.93
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:04:23.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4779.61
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:53.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.47
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:53.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4228.95
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:32.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11992.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:31.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.84
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000024625

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.79
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999897248

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:11.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   0.034
p-value of test                       :    0.49

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:40.10

 All tests were passed




Server wird beendet - Lösche Semaphor 105218069.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5481
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:50.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:38.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:37.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:55.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:01.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:03.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:54.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:58.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     831
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9935

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:12.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9915

Test on the Nm values of W_{n,i}(mNP1):    2.33
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:46.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.94
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.40
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.95
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.40
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.62
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.04
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.74
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.17
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1315.96
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7124.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.22
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:04.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.73
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.05
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:35.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4920.83
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:56.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46051
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870051
  j =  1                              :        399907903
  j =  2                              :            46041
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45695
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869695
  j =  1                              :        399908611
  j =  2                              :            45693
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:28.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:18.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 2.98e-3
p-value of test                       :    0.9969

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.55e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 3.62e-4
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:38.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:38.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.41
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:48.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.24
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.21
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.00
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.81
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   50.48
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.59
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17514.96
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.57
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.24
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.38
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.63
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.32
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.36
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.52
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.12
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.45
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.08
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.45
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.82
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.28
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.20
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.40
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.96
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.46
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.16
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.93
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.36
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.82
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.97
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.97
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.92
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.78
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.93
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:24.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.43
p-value of test                       :  9.3e-3


-----------------------------------------------
Normal statistic for number of jumps  :   -2.69
p-value of test                       :    0.9964



-----------------------------------------------
CPU time used                    :  00:02:25.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 5.23e-3
p-value of test                       :    0.9945

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.34
p-value of test                       :    0.9903

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
p-value of test                       :    0.9939

Anderson-Darling statistic = A2       :    4.25
p-value of test                       :  6.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.90
p-value of test                       :    0.9981

Sample variance                       :    0.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.24e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.23e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.37
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.44
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.41
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.96
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:07.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9912.06
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.04
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:04:04.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.77
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.41
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4012.93
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.58
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.82
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11838.02
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.40
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000023569

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.57
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999963626

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   0.040
p-value of test                       :    0.48

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:17.53

 All tests were passed




Server wird beendet - Lösche Semaphor 106233877.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5344
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:49.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:38.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7158
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:38.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:03.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:54.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:00.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.04
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:14.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:44.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.58
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.61
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.15
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.22
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.91
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:42.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7172.79
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.86
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.28
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:02.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.13
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.69
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5065.80
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:00.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45775
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869775
  j =  1                              :        399908455
  j =  2                              :            45765
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46149
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870149
  j =  1                              :        399907704
  j =  2                              :            46145
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:26.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:19.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9910


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:46.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:59.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.94e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 2.54e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:37.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.92
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   61.42
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:00:47.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.53
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.12
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:38.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.56
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.49
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.93
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.15
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.14
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17311.91
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.57
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.81
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.56
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.91
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.76
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.72
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.24
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.40
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.78
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.50
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.87
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.58
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.67
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.67
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.48
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.22
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.02
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.07
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.05
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.38
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.80
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.08
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4919.58
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  315.00
p-value of test                       :    0.9920


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.31
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.18
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.09
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5133.60
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.78
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.93
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.36
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:24.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.62
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:24.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    2.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.53e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 9.88e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.55
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.39
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.79
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:05.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.50
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:08.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10089.00
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10099.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:43.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4772.99
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4773.39
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:49.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.26
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11542.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12051.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.21
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999995105

Normal statistic for number of bits   :  -0.039
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   31.82
p-value of test                       :    0.9930


-----------------------------------------------
Total number of bits:  8000116836

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.44
p-value of test                       :    0.07

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:37.87

 All tests were passed




Server wird beendet - Lösche Semaphor 107249685.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9963


-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:52.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5431
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:51.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:39.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7112
p-value of test                       :    0.9922


-----------------------------------------------
CPU time used                    :  00:02:40.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:59.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:10.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:06.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:12.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:14.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:40.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   20.47
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.10
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.07
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.21
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.91
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.86
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:55.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1492.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:04.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7174.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.01
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:17.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.90
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:47.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:45.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5016.29
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:59.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46078
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870078
  j =  1                              :        399907847
  j =  2                              :            46072
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45822
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869822
  j =  1                              :        399908361
  j =  2                              :            45812
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:31.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:19.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:10.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.46e-4
p-value of test                       :    0.9994    *****

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:39.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.43e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 7.59e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9974

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 8.81e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.063
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.19
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.60
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.47
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.33
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.81
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.61
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17333.87
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.41
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.64
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.18
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.10
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.55
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.89
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.74
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.71
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.85
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.40
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.51
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.99
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  427.16
p-value of test                       :    0.9919


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.11
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.61
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.62
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.33
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.19
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.57
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.08
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.67
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.22
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5094.13
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.77
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.65
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.81
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.98
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4858.83
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.38
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.24
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.69
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:25.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.26
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    1.73
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:26.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.60
p-value of test                       :    0.94

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.13e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 5.14e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.45
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.50
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.48
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:06.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.42
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9912.25
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.30
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.087
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:04:31.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:55.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5073.52
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:59.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3970.12
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.67
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.31
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:37.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11666.68
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.97
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999971897

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.18
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000048430

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9939

Tests on the sum of all N observations
Standardized normal statistic         : 9.90e-3
p-value of test                       :    0.50

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:31.89

 All tests were passed




Server wird beendet - Lösche Semaphor 108265493.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1468
p-value of test                       :  2.8e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334588
  j =  1                              :        599997064
  j =  2                              :             1468
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5413
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:51.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:39.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4435
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:05.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7139
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:53.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:58.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    2.91
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:14.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.88
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    3.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:42.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.32
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.68
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.20
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  194.96
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.58
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:44.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1543.58
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:03.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7112.86
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:44.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.20e-3
p-value of test                       :    0.9934

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.82
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.06
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:34.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5114.86
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:53.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45529
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869529
  j =  1                              :        399908946
  j =  2                              :            45521
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45948
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869948
  j =  1                              :        399908107
  j =  2                              :            45942
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:26.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:19.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:39.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.77
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.70
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.79
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.14
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.89
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:29.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17533.80
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.05
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.28
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.49
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.56
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.92
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.68
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.02
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.73
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.42
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.68
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.46
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.82
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.59
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.69
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.49
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.84
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.01
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.55
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.30
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.33
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.00
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.68
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.35
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.14
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.76
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.24
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.64
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5094.59
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.26
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.44
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.75
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:22.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.74
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:24.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.00e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.39
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.52
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.56
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.19
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:06.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9934.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10173.11
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.56
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:44.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.55
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.83
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.57
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.23
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.87
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.41
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999828344

Normal statistic for number of bits   :   -1.36
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.78
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999959900

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   0.050
p-value of test                       :    0.48

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   0.087
p-value of test                       :    0.47

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   0.025
p-value of test                       :    0.49

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:36.29

 All tests were passed




Server wird beendet - Lösche Semaphor 109576213.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  1.2e-3


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1481
p-value of test                       :  9.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334601
  j =  1                              :        599997038
  j =  2                              :             1481
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5469
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:51.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:39.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7528
p-value of test                       :  7.4e-3


-----------------------------------------------
CPU time used                    :  00:03:04.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:55.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    3.13
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.16
p-value of test                       :    0.9978

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9962

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    3.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:13.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:41.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.74
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.77
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.67
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.91
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.84
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.77
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.41
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:02.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7106.84
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.72
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.75
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:04.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.08
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.68
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5100.98
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:54.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45257
p-value of test                       :    0.9982


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869257
  j =  1                              :        399909489
  j =  2                              :            45251
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45888
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869888
  j =  1                              :        399908230
  j =  2                              :            45876
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:28.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:17.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:35.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.83e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.86
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.05
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.24
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.13
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.52
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.02
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.20
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17525.62
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.97
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.38
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.06
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.25
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.71
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.11
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.17
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.67
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.65
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.54
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.03
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.31
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.69
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.92
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.59
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.55
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.45
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.35
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.78
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4879.58
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.03
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.99
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.70
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.93
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.84
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.41
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.21
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.89
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:22.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.81
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -1.81
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.78e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.10e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 8.47e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.87
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.00
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:05.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.88
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10019.41
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.038
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:43.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.00
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:49.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.92
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11957.61
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11824.73
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.98
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999987695

Normal statistic for number of bits   :  -0.097
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.24
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999999779

Normal statistic for number of bits   : -1.75e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:42.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           9.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 110493717.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:51.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7163
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:39.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4450
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:05.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:04.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:54.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:00.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:45.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.38
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:12.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.93
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:41.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.14
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.38
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.42
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.94
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.54
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.44
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.55
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.25
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.10
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.71
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:02.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7019.53
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:40.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.25
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.29
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:06.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.54
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   83.78
p-value of test                       :    0.9940


-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5069.75
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:54.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46060
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870060
  j =  1                              :        399907882
  j =  2                              :            46056
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45699
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869699
  j =  1                              :        399908602
  j =  2                              :            45699
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:27.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:18.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:01.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:34.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.35e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.15e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:35.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.35
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:48.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.46
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.52
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.29
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.92
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:39.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.92
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.80
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17477.77
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.08
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.85
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.12
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.06
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.91
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.64
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   15.40
p-value of test                       :    0.9983


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.14
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.35
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.50
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.31
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.68
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.89
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.91
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.42
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.98
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.03
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.84
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.48
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.82
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.18
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.92
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4848.16
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.13
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.99
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.16
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  464.90
p-value of test                       :  2.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.43
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.49
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.94
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.02
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   0.092
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.88
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :   -1.37
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:23.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.09e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.46e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.08
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.24
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.39
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:04.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.68
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:08.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9950.44
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9756.54
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:42.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.98
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4693.72
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.68
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.83
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11748.32
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11948.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.25
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999962843

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.55
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000062296

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:37.12

 All tests were passed




Server wird beendet - Lösche Semaphor 111312917.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5497
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:51.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7529
p-value of test                       :  7.2e-3


-----------------------------------------------
CPU time used                    :  00:02:38.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:06.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:06.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:58.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:02.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.53
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:13.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:39.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.74
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.21
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.73
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.35
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.18
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.76
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.75
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:52.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1406.03
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:04.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7128.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:52.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.93
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:10.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.95
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.34
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:37.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4966.53
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:54.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45990
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869990
  j =  1                              :        399908025
  j =  2                              :            45980
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45646
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869646
  j =  1                              :        399908710
  j =  2                              :            45642
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:30.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:19.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:05.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  1.4e-3

Anderson-Darling statistic = A2       :    4.49
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:01:55.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :  2.4e-3

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.48e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 8.32e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.13
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.92
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.67
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.63
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.43
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.69
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.81
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.90
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17247.65
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.02
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.80
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.51
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.90
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.66
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.42
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.47
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.57
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.39
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.76
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.70
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.91
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.01
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.72
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.38
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.59
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.27
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.67
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.67
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.98
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.28
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4896.02
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.71
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.75
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.90
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.69
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4739.44
p-value of test                       :    0.9959


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.75
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.75
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.27
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.74
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:20.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 5.09e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.24
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.86
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.61
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:07.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.77
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:04:17.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5095.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:54.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5060.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:54.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.21
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4251.54
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12004.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12238.18
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   28.59
p-value of test                       :    0.9983


-----------------------------------------------
Total number of bits:  8000050785

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.18
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999879284

Normal statistic for number of bits   :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:11.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:52.27

 All tests were passed




Server wird beendet - Lösche Semaphor 112295957.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:52.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:57.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:04.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:04.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:55.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:00.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:07.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    5.99
p-value of test                       :  1.0e-3    *****

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:36.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.80
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.93
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.21
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.75
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.78
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.93
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.79
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.34
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1352.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7221.92
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:42.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.98
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:05.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.82
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.47
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5039.86
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:57.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45871
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869871
  j =  1                              :        399908259
  j =  2                              :            45869
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46118
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870118
  j =  1                              :        399907773
  j =  2                              :            46100
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:27.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.8e-4    *****

Anderson-Darling statistic = A2       :    4.87
p-value of test                       :  3.4e-3


-----------------------------------------------
CPU time used                    :  00:02:17.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 4.67e-3
p-value of test                       :    0.9949

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:45.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:00.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:54.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 9.93e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:35.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.04
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.53
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.35
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.83
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.74
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:41.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.02
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.21
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17593.64
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.12
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.49
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.09
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.34
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.13
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.74
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.53
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.07
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.57
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.80
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.04
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  430.09
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.97
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.59
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.29
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.33
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.02
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.43
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.01
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.92
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.44
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.29
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.71
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.80
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.90
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.97
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.28
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.33
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.80
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.00
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -0.79
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.59
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:24.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.84e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.63e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 5.39e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.43
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.77
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:04.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:05.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10064.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10022.86
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:45.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.65
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:48.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.21
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.80
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11692.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.26
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.88
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000011620

Normal statistic for number of bits   :   0.092
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.97
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000154804

Normal statistic for number of bits   :    1.22
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.84
p-value of test                       :    0.03

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.15
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:33.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP2, t = 16         1.0e-3
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 113442837.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9987


-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:51.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:40.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:04.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:54.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:59.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.45
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:13.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:40.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.19
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.36
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.81
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.17
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.05
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.56
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  388.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:02.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6902.37
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.56
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:01.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.44
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.65
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:35.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5061.61
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:55.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46017
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870017
  j =  1                              :        399907969
  j =  2                              :            46011
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46286
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870286
  j =  1                              :        399907432
  j =  2                              :            46278
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 9.50e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:28.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:18.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:46.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 4.09e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 8.11e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:36.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:36.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.09
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.08
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.67
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.23
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.75
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.44
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.94
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.81
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17733.73
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.49
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.66
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.72
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.89
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.32
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.72
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.47
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.80
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.49
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.72
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.15
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.92
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.02
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.94
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.11
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.79
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.70
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.94
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.15
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.88
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.00
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  452.59
p-value of test                       :  9.0e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.19
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.43
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.31
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.06
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.75
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.18
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.73
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.60
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.62
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:23.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.38
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.95e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.75e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 9.47e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.22
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.80
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.56
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:06.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.3e-3

Anderson-Darling statistic = A2       :    5.33
p-value of test                       :  2.1e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  267.52
p-value of test                       :  1.0e-3

-----------------------------------------------
CPU time used                    :  00:02:05.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9909.53
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9871.12
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:41.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.82
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.44
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4188.29
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12144.84
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11968.30
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.68
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000070342

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.17
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000094525

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    2.49
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-3
p-value of test                       :    0.9986

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.67
p-value of test                       :  3.8e-3

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:51.56

 All tests were passed




Server wird beendet - Lösche Semaphor 114393109.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5492
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:54.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:40.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4226
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7161
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:03.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7148
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:03.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:55.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:00.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.94
p-value of test                       :  9.7e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.93
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    2.06
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:11.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:41.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.21
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.94
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.58
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.14
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.12
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.76
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.14
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.49
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:02.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6912.93
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:41.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.91
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.78
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:06.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.10
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.21
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5062.98
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:54.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46184
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870184
  j =  1                              :        399907636
  j =  2                              :            46176
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45795
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869795
  j =  1                              :        399908412
  j =  2                              :            45791
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:27.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:17.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:34.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.18
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:48.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.51
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.36
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.74
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:37.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.33
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.92
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17460.91
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.07
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.80
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.34
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.18
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.03
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.40
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.02
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.90
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.73
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.65
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.26
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  419.16
p-value of test                       :    0.9964


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.49
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.30
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.59
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.66
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.99
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.15
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.61
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.74
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.68
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.25
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.01
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.19
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.77
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.34
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4919.82
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.06
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.08
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.03
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    2.50
p-value of test                       :  6.2e-3



-----------------------------------------------
CPU time used                    :  00:02:25.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.08
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   -1.25
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:25.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    2.16
p-value of test                       :    0.02

Sample variance                       :    2.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.07e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 7.88e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.63e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.46
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.92
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.09
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:08.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.49
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:05.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.68
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:43.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5015.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.77
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:49.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.85
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.14
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11644.44
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11421.83
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   82.04
p-value of test                       :  8.3e-3


-----------------------------------------------
Total number of bits:  8000113491

Normal statistic for number of bits   :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.94
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000051814

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:55.30

 All tests were passed




Server wird beendet - Lösche Semaphor 115376149.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5334
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:53.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4226
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:05.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:05.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:57.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:59.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    2.23
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:12.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.08
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:40.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.35
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.24
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.45
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.75
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.92
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.73
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1492.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:06.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6859.89
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.83
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.36
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:08.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.90
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.50
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5103.04
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:00.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908048
  j =  2                              :            45970
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46166
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870166
  j =  1                              :        399907670
  j =  2                              :            46162
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:29.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:03.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:56.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.95
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:42.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.30
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.40
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.45
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.02
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:45.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.63
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.94
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.36
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17388.12
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.38
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.47
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.54
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.69
p-value of test                       :    0.9911


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.58
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.58
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.76
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.22
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.53
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   35.53
p-value of test                       :  5.3e-3


-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.09
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.06
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.17
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.65
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.76
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.89
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  193.39
p-value of test                       :  5.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.25
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.49
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.28
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.61
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.55
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.88
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  434.08
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  241.89
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.07
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.06
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4871.92
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.04
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.09
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.87
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -1.26
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:23.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.09
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :   -1.57
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:22.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 9.19e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.19e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.74
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.93
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.44
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:05.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:06.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.78
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10197.21
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:12.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5028.22
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:53.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.71
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:53.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.38
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4014.67
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.67
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11806.01
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.68
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999888401

Normal statistic for number of bits   :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.87
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000015421

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    2.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:25.43

 All tests were passed




Server wird beendet - Lösche Semaphor 116326421.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5415
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:56.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7136
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:08.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:08.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:06.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7100
p-value of test                       :    0.9947


-----------------------------------------------
CPU time used                    :  00:04:13.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     846
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:14.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:42.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.17
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.61
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.56
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.88
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.65
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:11.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7186.13
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.61
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.76
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:15.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.97
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.61
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:43.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4944.69
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:32.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:55.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45959
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869959
  j =  1                              :        399908083
  j =  2                              :            45957
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45738
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869738
  j =  1                              :        399908525
  j =  2                              :            45736
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:30.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:21.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:52.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:08.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.45e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.88e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.12e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.15e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:24.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.31
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.98
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.25
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:56.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.38
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.32
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.38
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17462.74
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.73
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.58
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.21
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.80
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.33
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.17
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.11
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.51
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.59
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.63
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.48
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.03
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.71
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.64
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.51
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.78
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.59
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.81
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.26
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.02
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.62
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.96
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.65
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.82
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.91
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4868.19
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.21
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.84
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:34.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.99
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:22.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.07
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:23.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 9.21e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.76e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.02
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.50
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:28.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.24
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:27.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9843.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10191.96
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:04:31.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4998.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:54.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4999.62
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.33
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.83
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.60
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:32.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.56
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000202696

Normal statistic for number of bits   :    1.60
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.97
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000185845

Normal statistic for number of bits   :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:14.37

 All tests were passed




Server wird beendet - Lösche Semaphor 117374997.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:48.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:57.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4530
p-value of test                       :  1.8e-3


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:42.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:01.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:12.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:06.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:08.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     638
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:15.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:42.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.04
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.74
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.77
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:35.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:34.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.77
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:33.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   83.63
p-value of test                       :  6.0e-3

-----------------------------------------------
CPU time used                    :  00:01:32.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  188.78
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:53.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1441.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:04.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6957.68
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.57
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.64
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   50.83
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.03
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.08
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.40
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4848.59
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:56.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46037
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870037
  j =  1                              :        399907929
  j =  2                              :            46031
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45777
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869777
  j =  1                              :        399908448
  j =  2                              :            45773
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:30.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:17.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:53.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9965

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:59.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.86e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.17
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.93
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.09
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.94
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.17
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.89
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17559.21
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.43
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.14
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.32
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.98
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   61.43
p-value of test                       :  5.2e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.50
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.36
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.80
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.73
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.52
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  209.11
p-value of test                       :  4.8e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.79
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.25
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.02
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.02
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.45
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.87
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.57
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.86
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.31
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.83
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.11
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.12
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.88
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4787.03
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.85
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.57
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.94
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:22.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.00
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:22.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.15e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.93
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.37
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.13
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:04.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.99
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:04.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9768.55
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9839.00
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:04:16.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.18
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:52.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.66
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.98
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.09
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.12
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:32.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.24
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000026212

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.57
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000034261

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:29.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 M (L=1000, r=0)     4.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 118751253.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:48.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5562
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:56.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:41.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:05.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:56.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:01.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:14.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:45.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.60
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.46
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.95
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.39
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.73
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.83
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.27
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.12
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.66
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:02.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6961.31
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.76
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.91
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:05.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.60
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:46.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.69
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4855.67
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:58.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46223
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870223
  j =  1                              :        399907559
  j =  2                              :            46213
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45949
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869949
  j =  1                              :        399908105
  j =  2                              :            45943
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :  4.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:28.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:19.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:59.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:35.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:36.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.062
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.63
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.10
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.83
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.55
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9951

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.43
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.10
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.07
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17642.09
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.74
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.90
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.98
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.18
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.68
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.54
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.25
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.07
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.27
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.75
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.07
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.43
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.33
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.85
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.67
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.95
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.22
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.13
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.02
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.37
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.58
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.52
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4879.97
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.53
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.18
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.55
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.09
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.68
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.11
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.79
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    1.40
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:21.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.57
p-value of test                       :    0.9900


-----------------------------------------------
Normal statistic for number of jumps  :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:22.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.07e-3
p-value of test                       :    0.9958

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.79
p-value of test                       :    0.9973

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.61e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.34e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.46
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.95
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.61
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:03.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:03.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10090.38
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.23
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:36.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4979.16
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.16
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:50.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4228.34
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.55
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12001.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11631.09
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.64
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999964280

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.02
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999932135

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    2.33
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:46.04

 All tests were passed




Server wird beendet - Lösche Semaphor 119832597.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997307
  j =  2                              :             1345
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:57.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:04.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:04.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:55.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:00.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    2.52
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     837
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.86
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.54
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    4.53
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:02:15.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    3.23
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:45.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.77
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.09
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.75
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.44
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7029.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.18
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.84
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.63
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.54
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:31.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4890.75
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:56.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46321
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870321
  j =  1                              :        399907361
  j =  2                              :            46315
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45982
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869982
  j =  1                              :        399908039
  j =  2                              :            45976
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.87e-3
p-value of test                       :    0.9955

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  2.9e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:28.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:18.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.53
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.52
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.64
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.00
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.00
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.35
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.22
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.66
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17368.01
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.45
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.96
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.00
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.80
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.29
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.15
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.41
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.73
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.49
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.72
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.76
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.41
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.19
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.73
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.35
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.23
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.49
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.90
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.88
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.99
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.55
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4823.74
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.06
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.17
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.78
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  455.81
p-value of test                       :  6.8e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.03
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.22
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.95
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.31
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:22.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.50
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    1.88
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 2.99e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.12
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.54
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.40
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:03.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  2.1e-3

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.72
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:03.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9869.56
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.55
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:39.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.85
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:49.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.03
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3989.23
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11932.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.28
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.69
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000112648

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.80
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000034687

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:17.72

 All tests were passed




Server wird beendet - Lösche Semaphor 120815637.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:56.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7138
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:41.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:05.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:55.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:00.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:17.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.92
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:46.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.95
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.09
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.72
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.73
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.08
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.98
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.58
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  481.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1469.31
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7048.28
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.84
p-value of test                       :  1.1e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    5.37
p-value of test                       :  2.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   11.93
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.02
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:02.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.51
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.94
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5187.38
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:58.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45808
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869808
  j =  1                              :        399908391
  j =  2                              :            45794
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45721
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869721
  j =  1                              :        399908559
  j =  2                              :            45719
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:28.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:18.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.05
p-value of test                       :  8.4e-3


-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:59.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:53.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.98e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:34.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.054
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:48.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.98
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.28
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.24
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.77
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.58
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.47
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17068.31
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:48.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.03
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.13
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.92
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.66
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:34.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.05
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.18
p-value of test                       :    0.9973


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.69
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.26
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.40
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.20
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.04
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.57
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  110.45
p-value of test                       :  3.9e-3


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.18
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.03
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.52
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.65
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.67
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.43
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.39
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.22
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.24
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  241.12
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.25
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.67
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.84
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.72
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.38
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.22
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:10.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.45
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    1.84
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:11.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.88e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.38
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.44
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:15.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.65
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:53.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.86
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9908.58
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.81
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:17.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4992.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:34.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4974.30
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.86
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.25
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.06
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.08
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000074329

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.07
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000045469

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.045
p-value of test                       :    0.52

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.03
p-value of test                       :    0.02

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:56:49.87

 All tests were passed




Server wird beendet - Lösche Semaphor 121831445.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9913


-----------------------------------------------
CPU time used                    :  00:00:48.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5539
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:41.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:35.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:33.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:53.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:54.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:00.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:00.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:53.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:58.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     944
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.85
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.58
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:10.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:32.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.68
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.96
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.47
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  481.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7102.70
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9910

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:02.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.44
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.93
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5015.90
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:10.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45713
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869713
  j =  1                              :        399908577
  j =  2                              :            45707
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45825
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869825
  j =  1                              :        399908352
  j =  2                              :            45821
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:27.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:16.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:59.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:52.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:33.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.42
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.055
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.040
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:38.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.43
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.90
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.12
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.51
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.91
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.85
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:32.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.34
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17170.37
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.66
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.22
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.24
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.40
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.13
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.53
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.84
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.64
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.89
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.29
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.96
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.31
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  590.37
p-value of test                       :  3.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.71
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.71
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.80
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.07
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.66
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.13
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:48.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.20
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.82
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.46
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.53
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.45
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.93
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.06
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.64
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.40
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.87
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:14.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.97
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:12.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 5.85e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:47.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.75e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.19
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.08
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.60
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:10.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.53
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:10.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10019.09
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9869.69
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.060
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:45.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.76e-5
p-value of test                       : 1 -  6.8e-5    *****

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.7e-3

Anderson-Darling statistic = A2       :    3.97
p-value of test                       :  9.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5194.03
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:01:48.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4724.99
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.77
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3977.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12126.37
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.10
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:29.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.23
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000005869

Normal statistic for number of bits   :   0.046
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.65
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999850394

Normal statistic for number of bits   :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:35.04

 All tests were passed




Server wird beendet - Lösche Semaphor 102301718.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9946


-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:56.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1483
p-value of test                       :  7.8e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334603
  j =  1                              :        599997034
  j =  2                              :             1483
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:42.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4223
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:37.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:35.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:54.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:00.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:01.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:52.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:58.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     856
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     543
p-value of test                       :    0.9903

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.65
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:10.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.88
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:37.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.56
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.24
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.58
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.13
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.35
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.69
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7089.74
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.07
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.77
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:03.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   16.49
p-value of test                       :  5.6e-3


-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.90
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:34.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5059.26
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45996
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869996
  j =  1                              :        399908012
  j =  2                              :            45988
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45831
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869831
  j =  1                              :        399908338
  j =  2                              :            45831
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:30.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:19.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.82
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:53.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:33.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.74e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:34.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:35.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.47
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:48.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.10
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.63
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.02
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.03
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.70
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.6e-3

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.68
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 5.29e-3
p-value of test                       :    0.9945

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17669.28
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.41
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.40
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.65
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.20
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.90
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.55
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.11
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.43
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.55
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.91
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.85
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.43
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  431.42
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.39
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.10
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.62
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.31
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  576.13
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.59
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.94
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.29
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5162.94
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.98
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.10
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.39
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.21
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.41
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.34
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.00
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:17.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.07
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:18.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :  -0.098
p-value of test                       :    0.54

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 6.35e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.10
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.32
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:10.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.72
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:08.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.94
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.37
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.62
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:48.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.98
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.88
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4656.97
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4022.94
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.41
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.90
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11699.66
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.77
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000121795

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.90
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000165919

Normal statistic for number of bits   :    1.31
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   0.066
p-value of test                       :    0.47

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:25.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           7.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 103055382.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:51.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:44.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:36.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:34.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:54.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:54.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:00.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:01.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:53.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:58.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    6.15
p-value of test                       :  8.4e-4    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     358
p-value of test                       :  6.2e-4    *****

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:09.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.82
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:39.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.39
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.40
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  480.00
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7048.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.10
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.59
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.41
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.48
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5096.77
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:11.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45839
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869839
  j =  1                              :        399908328
  j =  2                              :            45827
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46044
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870044
  j =  1                              :        399907916
  j =  2                              :            46036
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:29.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:18.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:55.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.021
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:35.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:35.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.76
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.86
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.77
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.80
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.99
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17480.92
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.61
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.65
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.01
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.06
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.13
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.11
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.11
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.71
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.67
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.36
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.46
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.91
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.92
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.47
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.72
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.40
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.38
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.91
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.33
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.04
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.22
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5162.51
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.85
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.62
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.31
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:19.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.26
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    2.25
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:02:20.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.28
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.06
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.02
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:07.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.04
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.16
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10114.14
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:40.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4728.41
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.46
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3948.65
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11926.83
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11915.64
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.73
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999959927

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.76
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000014353

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.78e-4
p-value of test                       :    0.9993    *****

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.96
p-value of test                       :    0.03

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   0.073
p-value of test                       :    0.47

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   0.059
p-value of test                       :    0.48

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:52.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP1, t = 9          8.4e-4
 24  ClosePairs NJumps, t = 9        6.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 103907350.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5317
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:46.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:38.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:37.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4146
p-value of test                       :    0.9982


-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:03.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:02.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:51.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:57.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    4.40
p-value of test                       :  5.6e-3

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:13.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:39.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.18
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.05
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.56
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.02
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.48
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  385.82
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1331.84
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7059.36
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.41
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:06.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.66
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.42
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4903.39
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:08.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45955
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869955
  j =  1                              :        399908095
  j =  2                              :            45945
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45887
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869887
  j =  1                              :        399908231
  j =  2                              :            45877
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  6.0e-3

Kolmogorov-Smirnov- statistic = D-    : 5.06e-3
p-value of test                       :    0.9938

Anderson-Darling statistic = A2       :    4.85
p-value of test                       :  3.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9987


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:27.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:18.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:45.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:03.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.00e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.09
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.29
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.90
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.05
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.65
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:41.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.2e-3

Kolmogorov-Smirnov- statistic = D-    : 6.59e-3
p-value of test                       :    0.9930

Anderson-Darling statistic = A2       :    6.21
p-value of test                       :  8.4e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   15.73
p-value of test                       :    0.9998    *****

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   11.94
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.73
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17631.93
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.24
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.35
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.17
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.31
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.29
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.07
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.39
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.92
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.90
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.89
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.62
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.78
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.45
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.91
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.79
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.21
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.16
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  170.27
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.59
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.66
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.77
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.34
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.68
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.84
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.17
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.91
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.35
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.45
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.42
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.26
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:19.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.47
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -1.91
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:18.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 4.32e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.26e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.84
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.07
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.12
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10139.78
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.17
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:43.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.05
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.66
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4204.75
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4046.04
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.01
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11618.76
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.98
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999963782

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.23
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000018709

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.019
p-value of test                       :    0.51

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:52.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 67  MatrixRank, L=30, r=26          0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 104824854.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5432
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:57.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:43.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7487
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:06.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:05.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:51.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:56.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.03
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.66
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.60
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.36
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.72
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.70
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.16
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.84
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:58.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.78
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:01.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7159.02
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:05.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.70
p-value of test                       :  2.6e-3

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.46
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:05.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.92
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.06
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5004.97
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:55.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45923
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869923
  j =  1                              :        399908157
  j =  2                              :            45917
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46036
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870036
  j =  1                              :        399907931
  j =  2                              :            46030
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:27.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:17.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:00.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:33.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.76e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.92e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -3.94
p-value of test                       : 1 -  4.1e-5    *****

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:32.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.088
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:34.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.93
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.65
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.32
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.42
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.92
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:38.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.15
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.29
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.86
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   98.93
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17604.33
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.64
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.30
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.69
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.77
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.58
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.16
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.09
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.36
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.02
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.27
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.74
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.44
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.75
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.73
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.65
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.17
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.59
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.60
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.39
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.46
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.98
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.68
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.06
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.38
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.33
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.82
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.00
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.61
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  435.63
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.87
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:34.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.44
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:19.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.88
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   0.030
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:21.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.62e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.34e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.85
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.89
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.56
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:11.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:12.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9823.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10024.51
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:40.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5048.00
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
p-value of test                       :    0.9903

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4693.39
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3887.55
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.42
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.23
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11608.98
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.15
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999971405

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.92
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000049168

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :  -0.081
p-value of test                       :    0.53

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:57.18
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 55  SampleCorr, k = 1              1 -  4.1e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 105840662.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:55.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:41.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4528
p-value of test                       :  2.0e-3


-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:03.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:02.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:52.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:57.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:11.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.93
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:40.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.25
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.81
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.11
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.86
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.18
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.67
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:44.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.99
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7005.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.85
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.82
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.44
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5033.67
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:00.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45959
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869959
  j =  1                              :        399908083
  j =  2                              :            45957
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45643
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869643
  j =  1                              :        399908714
  j =  2                              :            45643
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:28.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:18.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.58e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 2.69e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 4.44e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:34.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:32.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.47
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.32
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.61
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
p-value of test                       :    0.9924

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   63.91
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.18
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.76
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17231.51
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.97
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.05
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.82
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.82
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.85
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.66
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.89
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.89
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.96
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.15
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.14
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.57
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.22
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.37
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.15
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.32
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.58
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.61
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.84
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.10
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.66
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.49
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.58
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.62
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.12
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.63
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.04
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.43
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.23
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :  -0.086
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:20.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.21
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:22.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.41e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.05e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.64
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.57
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.38
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:06.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.10
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.28
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10019.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.070
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:41.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5033.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.06
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.05
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.11
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11840.99
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.62
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000035572

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.08
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999950504

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:45.06

 All tests were passed




Server wird beendet - Lösche Semaphor 106823702.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:55.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7164
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7108
p-value of test                       :    0.9931


-----------------------------------------------
CPU time used                    :  00:03:04.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:04.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:52.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:57.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9910

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:45.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.01
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:10.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:36.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.90
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.93
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.67
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.33
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.70
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.81
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  392.70
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1342.37
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7108.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:42.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9929

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.75
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.36
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:07.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.02
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.80
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5034.05
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9994    *****


-----------------------------------------------
CPU time used                    :  00:02:53.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45944
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869944
  j =  1                              :        399908114
  j =  2                              :            45940
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45835
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869835
  j =  1                              :        399908334
  j =  2                              :            45827
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:28.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:19.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:46.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.55e-3
p-value of test                       :    0.9946

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:55.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.31e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.89e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:34.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:33.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.93
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:48.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.69
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.61
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.02
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:36.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.40
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.01
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.49
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17601.04
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.90
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.18
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.75
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.59
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.52
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.75
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.78
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.21
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.07
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.75
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.47
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.52
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.26
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  436.89
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.61
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.57
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.01
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.79
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5149.72
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.20
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.40
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.08
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.78
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.68
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.91
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.37
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.91
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:20.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.57
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:22.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.67e-3
p-value of test                       :    0.9962

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.86
p-value of test                       :    0.97

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 7.82e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 6.50e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.00
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.56
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.87
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:06.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.88
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10246.22
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10110.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:41.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.39
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4740.09
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.11
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3984.65
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.50
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11773.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.24
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999928487

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.98
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999900359

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.59

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:07.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 43  Permutation, t = 10             0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 107773974.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:57.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7523
p-value of test                       :  8.7e-3


-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:59.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:08.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:06.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:53.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:55.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.86
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9949

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:12.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:40.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.05
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:11.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.27
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.56
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.85
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.76
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.83
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:47.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.02
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:05.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7168.43
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.35
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.39
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:07.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.96
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.29
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:37.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5091.74
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:55.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45838
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869838
  j =  1                              :        399908326
  j =  2                              :            45834
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45895
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869895
  j =  1                              :        399908215
  j =  2                              :            45885
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:29.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:19.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:04.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.67e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.94
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.25
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.19
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.91
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.01
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:46.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.96
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.074
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  1.8e-3

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17846.12
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.67
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.51
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.90
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.98
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.29
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.69
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.57
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.43
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.66
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.44
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.62
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.06
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.03
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.44
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.66
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.88
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  172.26
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.84
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.29
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5086.85
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.15
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.56
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.51
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.13
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.51
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.86
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.91
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.07
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:22.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.61
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    1.98
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.11
p-value of test                       :    0.98

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 3.11e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.78e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.31
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.85
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.58
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:04.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.79
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:06.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9807.25
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10121.77
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:04:19.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.36
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:53.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.19
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:54.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3976.79
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11953.54
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11479.69
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:31.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   87.33
p-value of test                       :  2.7e-3


-----------------------------------------------
Total number of bits:  8000071581

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.99
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999956084

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.75
p-value of test                       :    0.04

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    2.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:04.86

 All tests were passed




Server wird beendet - Lösche Semaphor 108789782.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9907


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1477
p-value of test                       :  1.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334597
  j =  1                              :        599997046
  j =  2                              :             1477
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5472
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:56.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7050
p-value of test                       :    0.9992    *****


-----------------------------------------------
CPU time used                    :  00:02:41.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:04.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:03.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:54.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:00.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:46.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:10.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:42.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.39
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.02
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.87
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.23
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.39
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6986.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.70
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.67
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:04.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.73
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  159.41
p-value of test                       :  7.9e-3


-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.43
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:54.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46017
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870017
  j =  1                              :        399907970
  j =  2                              :            46009
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46022
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870022
  j =  1                              :        399907959
  j =  2                              :            46016
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:27.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:18.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:32.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.84e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.53
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:32.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:37.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  107.86
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   99.12
p-value of test                       :  6.6e-3

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.22
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.13
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.41
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:36.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9953

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.75
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.15
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.61
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.90
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17397.87
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.18
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.73
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.28
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.14
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.70
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.58
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.85
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.43
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.21
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.87
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.55
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.88
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.81
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.98
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.40
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.92
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.46
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.97
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.59
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.11
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.50
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.32
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.40
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.39
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.60
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.87
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.45
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.35
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.14
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.58
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:23.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.24
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.79
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:23.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :  7.7e-4    *****

Anderson-Darling statistic = A2       :    5.25
p-value of test                       :  2.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.85
p-value of test                       :  2.2e-3

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    2.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 6.01e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.03e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.92
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.11
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.51
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:04.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:03.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9848.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10103.44
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.55
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:40.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.70
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.17
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.81
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.57
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11856.12
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11643.35
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.21
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999951353

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.03
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999988244

Normal statistic for number of bits   :  -0.093
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:25.78
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 15  BirthdaySpacings, t = 4         0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 109805590.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5536
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:58.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:05.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:05.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:54.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:59.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     943
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    4.25
p-value of test                       :  6.6e-3

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    2.18
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     543
p-value of test                       :    0.9903

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:12.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.02
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:42.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.58
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.43
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.51
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.15
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.71
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.86
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1407.18
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:00.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7116.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.17
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.41
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:08.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.80
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.96
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:33.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5081.16
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:53.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45441
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869441
  j =  1                              :        399909122
  j =  2                              :            45433
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46039
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870039
  j =  1                              :        399907925
  j =  2                              :            46033
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:27.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:18.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:00.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 2.72e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.88e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:31.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.11
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:47.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.81
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.70
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:48.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.86
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.46
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.47
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:39.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.96
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.80
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.12
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17464.07
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.87
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.90
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.80
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.20
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.74
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.06
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.58
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.39
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.47
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.01
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.86
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.15
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.79
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.74
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.32
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.67
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.80
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.62
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.55
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.91
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.20
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.64
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.04
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.79
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.28
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.42
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.84
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.94
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :   0.079
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:22.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.59
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :  -0.042
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:24.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 5.89e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.07e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.95
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.52
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.06
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:03.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.78
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:04.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10218.78
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:39.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:48.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.53
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:50.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.79
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4265.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.11
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11580.15
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.47
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999977456

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.72
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000083698

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    2.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:06.20

 All tests were passed




Server wird beendet - Lösche Semaphor 110821398.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5529
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:57.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:42.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:05.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:05.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:55.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7473
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:00.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    5.25
p-value of test                       :  2.2e-3

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:12.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.44
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    2.83
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:43.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.58
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.76
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.47
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.78
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.66
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.16
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.35
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.51
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:46.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1505.42
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:01.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7080.40
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:44.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.78
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:01.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.68
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.53
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5180.83
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:52.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45993
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869993
  j =  1                              :        399908021
  j =  2                              :            45979
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869769
  j =  1                              :        399908467
  j =  2                              :            45759
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:27.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:19.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:02.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:55.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 5.72e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.65e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:34.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:32.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.66
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.53
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.71
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.14
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:38.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.73
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.03
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.35
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.64
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17559.19
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.62
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.89
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.35
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.57
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.80
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.64
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.19
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.44
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.04
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.65
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.87
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.26
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.25
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.19
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.84
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.69
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.41
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.87
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.18
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.52
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.82
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.29
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.48
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.83
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.13
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.82
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.98
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5090.50
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.05
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.17
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.62
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:20.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.83
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:21.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.83
p-value of test                       :    0.97

Sample variance                       :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.21e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.68e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.91
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.80
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.91
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:05.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:05.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10143.09
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9733.67
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:38.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.76e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5160.48
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:01:47.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4254.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11641.56
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11759.93
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.25
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999978920

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.35
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000029656

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.60
p-value of test                       :    0.95

Sample variance                       :    2.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:14.98

 All tests were passed




Server wird beendet - Lösche Semaphor 111804438.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5362
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:58.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:44.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4232
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4242
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7158
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:05.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:56.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7470
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:00.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.38
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9937

-----------------------------------------------
CPU time used                    :  00:02:05.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:34.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.28
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.38
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.83
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.38
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.56
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  192.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.35
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.10
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:01.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7037.43
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.49
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:05.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.75
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.33
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4984.30
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:11.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:50.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45788
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869788
  j =  1                              :        399908428
  j =  2                              :            45780
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45717
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869717
  j =  1                              :        399908572
  j =  2                              :            45705
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:27.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:59.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:33.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 2.58e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 4.71e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:32.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.55
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:48.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.01
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.98
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:39.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.54
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.63
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.46
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.14
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9953

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.44
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17526.04
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.26
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.92
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.50
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.35
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.51
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.43
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.36
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.78
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.44
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.93
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.22
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.67
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.62
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.27
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.33
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.68
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  584.64
p-value of test                       :  5.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.45
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.97
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.25
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.44
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5076.04
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.35
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.38
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.00
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.21
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5118.79
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.56
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.07
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.95
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:21.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.62
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -1.28
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:22.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.36
p-value of test                       :  9.2e-3

Sample variance                       :    2.85
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.20
p-value of test                       :    0.99

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.68e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.45e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 5.92e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.88
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.19
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.62
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:03.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.99
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:04.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10175.70
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9917.25
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:41.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:51.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3977.93
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11724.73
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11441.74
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:01:29.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.47
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000056332

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.79
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000090916

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.19
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.82
p-value of test                       :    0.03

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:50.22

 All tests were passed




Server wird beendet - Lösche Semaphor 112820246.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9988


-----------------------------------------------
CPU time used                    :  00:00:40.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1475
p-value of test                       :  1.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334595
  j =  1                              :        599997050
  j =  2                              :             1475
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5490
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:03.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:44.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:47.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:02.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:02.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:11.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:11.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7524
p-value of test                       :  8.5e-3


-----------------------------------------------
CPU time used                    :  00:04:08.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:09.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:14.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :   0.084
p-value of test                       : 1 -  2.0e-6    *****

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:41.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.11
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.55
p-value of test                       :    0.9934

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.43
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.49
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.93
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.44
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:05.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6871.09
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:53.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.13
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.77
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:12.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.18
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.04
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:38.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5012.75
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:53.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45667
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869667
  j =  1                              :        399908669
  j =  2                              :            45661
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45605
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869605
  j =  1                              :        399908796
  j =  2                              :            45593
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:32.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:20.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:08.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.52e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.99e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:40.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.64
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.09
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.05
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.04
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.78
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:51.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.40
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.93
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17160.56
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   60.81
p-value of test                       :  4.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.21
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.99
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.10
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.29
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.46
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.37
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.17
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.43
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.04
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.58
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.59
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.23
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.29
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  104.10
p-value of test                       :    0.9965


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.25
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.98
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.17
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.59
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.35
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.66
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.75
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.12
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.55
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.56
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.08
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.08
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.15
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   -1.41
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:22.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.72
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:20.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.88e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.71e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.24
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.92
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.42
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:04.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.01
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:06.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10102.42
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9828.17
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:04:23.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5015.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:56.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5100.63
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:58.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.48
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.12
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12134.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:34.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:35.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.96
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000031522

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.40
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999983420

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:39.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP2, t = 16        1 -  2.0e-6
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 113803286.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5514
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:57.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:43.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:58.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:05.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:06.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:55.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:58.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     555
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    2.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:11.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.28
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:41.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.51
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.14
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.35
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.09
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.84
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.99
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.26
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.87
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6840.10
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.21
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.43
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:07.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.65
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   84.55
p-value of test                       :    0.9929


-----------------------------------------------
CPU time used                    :  00:01:32.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.98
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:51.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45830
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869830
  j =  1                              :        399908344
  j =  2                              :            45822
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45813
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869813
  j =  1                              :        399908379
  j =  2                              :            45803
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:27.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:17.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.0e-3

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:55.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.78e-3
p-value of test                       :    0.9948

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :  2.3e-3

Anderson-Darling statistic = A2       :    4.72
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:01:33.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.04e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.058
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:32.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.96
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:48.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.97
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.16
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.69
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:48.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.29
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.81
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.18
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:41.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.10
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.26
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17580.10
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.30
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.46
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.82
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.18
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.09
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.78
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.37
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.39
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.03
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.28
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.94
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.31
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.48
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.88
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.01
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.31
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.82
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.93
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.75
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.44
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.99
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.51
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.53
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.97
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.66
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.48
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.53
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.23
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:20.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.77
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    1.60
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:21.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 4.52e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.01e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.16
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.19
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.26
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:03.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:03.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9780.70
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:40.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5011.99
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.40
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.12
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4051.66
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11760.05
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11711.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.02
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999914192

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.67
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000170824

Normal statistic for number of bits   :    1.35
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:47.82

 All tests were passed




Server wird beendet - Lösche Semaphor 114884630.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5392
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:56.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:42.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4458
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:05.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:06.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:55.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:59.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    2.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.51
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:12.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.05
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.88
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.85
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.06
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:44.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.19
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:01.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7073.11
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.50
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.52
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:02.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.85
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.09
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:34.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5239.95
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:56.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45535
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869535
  j =  1                              :        399908937
  j =  2                              :            45521
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45851
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869851
  j =  1                              :        399908302
  j =  2                              :            45843
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:28.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:45.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.12e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.99e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.60e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:34.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.30
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.01
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.08
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.67
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.07
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.06
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:38.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.50
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.5e-3

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  169.71
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17563.41
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.77
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.62
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.76
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.08
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.51
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.94
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.97
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.53
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.75
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.28
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.00
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.20
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.61
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.05
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.54
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.98
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.29
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.37
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.61
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.96
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.48
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.66
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.16
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.70
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.10
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.37
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.53
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.85
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.59
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.60
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:21.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.91
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :    1.79
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:22.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.54e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.52e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.06
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.94
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:03.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.05
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:02.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10151.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.01
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:41.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11729.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.93
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999949679

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.62
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000191752

Normal statistic for number of bits   :    1.52
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.99
p-value of test                       :    0.98

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:01.44

 All tests were passed




Server wird beendet - Lösche Semaphor 115867670.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5344
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:57.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:58.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:06.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:06.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:56.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:04:00.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     855
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.17
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    2.90
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     339
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:11.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.15
p-value of test                       :    0.9986


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    2.51
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    2.70
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:38.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.49
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.64
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.97
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.08
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.83
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.48
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  391.37
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1455.79
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:02.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7021.51
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.41
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.62
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:03.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.43
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.11
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4922.10
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:52.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46045
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870045
  j =  1                              :        399907914
  j =  2                              :            46037
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46011
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870011
  j =  1                              :        399907985
  j =  2                              :            45997
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:27.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:18.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:01.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:32.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.79e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.91
p-value of test                       :  1.8e-3

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.66
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.18
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.83
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.08
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.90
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17529.90
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.29
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.60
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.80
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.25
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.63
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.42
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.83
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.03
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.95
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.48
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.75
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.32
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.11
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.20
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.82
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.59
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.41
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.66
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.11
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.43
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.69
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.67
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  161.48
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.33
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.02
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.77
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.14
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.12
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.69
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:22.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.98
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.79e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 6.37e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.22
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.32
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.81
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:03.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.10
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:02.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9871.38
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10167.12
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.049
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.068
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:41.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.24
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5001.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.32
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11855.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.85
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000006571

Normal statistic for number of bits   :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.75
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999882578

Normal statistic for number of bits   :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   0.031
p-value of test                       :    0.49

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:58.05

 All tests were passed




Server wird beendet - Lösche Semaphor 116850710.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5353
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:58.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:43.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:58.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:06.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:05.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:56.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:02.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:51.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.10
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:16.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:47.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.43
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.38
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.00
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.43
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.72
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.71
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:44.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.07
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:01.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7247.36
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.63
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:04.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.17
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.13
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.49
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:52.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46193
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870193
  j =  1                              :        399907619
  j =  2                              :            46183
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45724
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869724
  j =  1                              :        399908556
  j =  2                              :            45716
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:26.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:18.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:02.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.89e-3
p-value of test                       :    0.9968

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:53.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:32.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.10e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 7.90e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.81
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:47.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.96
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.31
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.59
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.48
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17738.33
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.03
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.69
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.55
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.71
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.77
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.32
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.35
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.96
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.24
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.28
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.31
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.24
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.75
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.53
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.26
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.05
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.99
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.47
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.95
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.54
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5088.26
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.54
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.69
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.74
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.10
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5122.90
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.50
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.96
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.17
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:23.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.29
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.13e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.12
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.87
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.57
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:02.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.84
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:03.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9878.98
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10201.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:40.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.51
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3951.16
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4272.05
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11955.11
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.66
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.43
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000016159

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.65
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999937754

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.096
p-value of test                       :    0.46

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.27e-3
p-value of test                       :    0.9987

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.38
p-value of test                       :    0.9914

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.51

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:37.21

 All tests were passed




Server wird beendet - Lösche Semaphor 117866518.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5487
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:00.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:44.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:46.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:02.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:02.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:13.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:07.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:12.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:51.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    3.89
p-value of test                       :  9.8e-3

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.07
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    2.09
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:19.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    2.98
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.57
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.81
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.19
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.24
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  476.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:05.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.62
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:51.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.84
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.97
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.91
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5023.08
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:52.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46060
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870060
  j =  1                              :        399907883
  j =  2                              :            46054
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45855
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869855
  j =  1                              :        399908292
  j =  2                              :            45851
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:29.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:17.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:03.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.37e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.90
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.68
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.30
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.94
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.90
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:50.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.14
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.66
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17501.36
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.68
p-value of test                       :    0.9955


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.94
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.92
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.36
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.46
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.43
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.43
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.38
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.23
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.81
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.22
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.05
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.78
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.91
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.58
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.02
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.50
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.59
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.46
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.30
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.90
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.62
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.00
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.70
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.25
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.39
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5157.34
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.90
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.86
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.21
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:21.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.05
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    1.76
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:19.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 6.58e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.10e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.36
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.41
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.36
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:05.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.27
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:06.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10227.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9739.16
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:04:20.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.91
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:54.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:55.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.41
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.83
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11776.92
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:33.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.61
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:34.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.67
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999915827

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.49
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999884177

Normal statistic for number of bits   :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:44.79

 All tests were passed




Server wird beendet - Lösche Semaphor 118882326.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:57.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:43.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4197
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:59.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:07.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:07.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:55.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:00.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    8.77
p-value of test                       :  5.2e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:50.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    3.65
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.42
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:17.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:43.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.06
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.40
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.48
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.85
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.60
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.58
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.22
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.36
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:44.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:01.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6969.04
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:43.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9944

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.28
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:05.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.03
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.07
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:29.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5116.36
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:56.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46236
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870236
  j =  1                              :        399907531
  j =  2                              :            46230
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45925
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869925
  j =  1                              :        399908153
  j =  2                              :            45919
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:27.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:16.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:44.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:01.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:54.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:32.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.77e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.35e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:37.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.072
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.73
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.52
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.67
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.29
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:40.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.52
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.95
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.26
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17322.54
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.19
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.37
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.76
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.56
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.99
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.41
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.41
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.35
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.02
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.40
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.07
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.12
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.97
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.80
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.97
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.54
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.11
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.46
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.62
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  320.40
p-value of test                       :    0.9921


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.77
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.31
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  243.71
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.12
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.60
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.35
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.53
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.44
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.34
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:21.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.16
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:23.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.88

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 5.43e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 8.33e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.30
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.39
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.17
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:05.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:06.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.68
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:35.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.79
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.07
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.73
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11804.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.94
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000026578

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.68
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999901187

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    2.84
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:23.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP2S, t = 3         5.2e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 120029206.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997369
  j =  2                              :             1314
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:57.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:44.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:09.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:06.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:58.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:00.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.61
p-value of test                       :  1.5e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     939
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:51.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    3.83
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:18.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:45.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.78
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.97
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.05
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.06
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.34
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.51
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.67
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:42.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.64
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:03.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7066.68
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.21
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:03.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.54
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.92
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5001.25
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:59.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45803
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869803
  j =  1                              :        399908401
  j =  2                              :            45789
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45860
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869860
  j =  1                              :        399908284
  j =  2                              :            45852
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:27.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:18.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:44.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:59.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:55.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:35.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.52e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 2.67e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:39.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.47
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.19
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.70
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.84
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.01
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.99
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 4.66e-3
p-value of test                       :    0.9951

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.68
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.71
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.52
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17319.66
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.43
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.98
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.40
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.83
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.91
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.43
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.09
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.12
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.15
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.75
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.06
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.99
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.36
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.35
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.70
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.44
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.97
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  460.67
p-value of test                       :  4.3e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.16
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5104.03
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.62
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.06
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.70
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.00
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5106.90
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.55
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  249.19
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.43
p-value of test                       :    0.9916


-----------------------------------------------
Normal statistic for number of jumps  :   0.097
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.88
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 5.99e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.05e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.20
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.79
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:04.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.71
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:05.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10080.06
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10022.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.062
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:49.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.50
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5001.21
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:50.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12138.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11732.13
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:30.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.63
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999986579

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.57
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000082663

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:17.34

 All tests were passed




Server wird beendet - Lösche Semaphor 121012246.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1259
p-value of test                       :    0.9979

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334379
  j =  1                              :        599997482
  j =  2                              :             1259
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5599
p-value of test                       :  8.2e-3


-----------------------------------------------
CPU time used                    :  00:03:41.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4527
p-value of test                       :  2.1e-3


-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:34.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:00.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:00.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:53.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:58.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.24
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:51.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.26
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:10.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:34.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.26
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.18
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.25
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.35
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.75
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1353.66
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:02.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6982.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:47.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.64
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:02.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.67
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.61
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5089.25
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:13.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46135
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870135
  j =  1                              :        399907734
  j =  2                              :            46127
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45765
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869765
  j =  1                              :        399908472
  j =  2                              :            45761
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:27.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:17.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:44.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:58.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:53.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.98e-3
p-value of test                       :    0.9907

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:35.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:36.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.10
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.09
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.29
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.28
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:44.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.96
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.22
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:32.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:30.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.92
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  2.8e-3

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17735.02
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.60
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.62
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.18
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.70
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.39
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:40.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.03
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.02
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.57
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.09
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.13
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.85
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.52
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.41
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.83
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:47.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.99
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.54
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.82
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.64
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.79
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:47.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.45
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.26
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.31
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.29
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.41
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.10
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.71
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.03
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.85
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.95
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:34.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.80
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:12.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.27
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:12.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:11.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.41e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:47.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.64e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.00
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.01
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.20
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:09.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.73
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:10.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.61
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9893.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:45.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.72
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:50.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.03
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3902.75
p-value of test                       :    0.9917

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12016.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11824.96
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.84
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999902033

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.19
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999919940

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :  -0.070
p-value of test                       :    0.53

Sample variance                       :    0.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:29.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:54.50

 All tests were passed




Server wird beendet - Lösche Semaphor 102334487.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5353
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:43.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:34.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:54.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:54.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7523
p-value of test                       :  8.7e-3


-----------------------------------------------
CPU time used                    :  00:03:01.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:01.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7516
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:53.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:58.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:10.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.45
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    2.95
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    3.65
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:38.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.62
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.27
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.25
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.01
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.46
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.19
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.66
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.39
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.08
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.13
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:01.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6896.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.89
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.71
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:03.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.93
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.27
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:34.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5087.07
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:10.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46119
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870119
  j =  1                              :        399907764
  j =  2                              :            46115
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46196
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870196
  j =  1                              :        399907614
  j =  2                              :            46184
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:28.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:17.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:00.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:52.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:33.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 8.25e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.43
p-value of test                       :    0.9925

-----------------------------------------------
CPU time used                    :  00:01:38.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.035
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.49
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:48.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.55
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.19
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.01
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.38
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.89
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17513.62
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:55.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.47
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.29
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.49
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.39
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.03
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.65
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.31
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.08
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.85
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.59
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.12
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.27
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.08
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.11
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.55
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.32
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  576.61
p-value of test                       :  9.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.81
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.75
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.60
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.93
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.39
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.93
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.23
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.42
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.93
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.27
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.57
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.23
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:34.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.66
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:17.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.70
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    1.90
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:17.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.18
p-value of test                       :    0.01

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.16e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 6.74e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.36
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.05
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:09.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:08.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.45e-3
p-value of test                       :    0.9920

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10259.46
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:45.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.48
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.03
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:50.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3976.18
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.01
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11674.28
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12044.47
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.67
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999944363

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.90
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000013699

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         : 5.54e-3
p-value of test                       :    0.50

Sample variance                       :    0.21
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:39.73

 All tests were passed




Server wird beendet - Lösche Semaphor 103186455.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:43.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:36.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:35.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:54.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4463
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:01.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:01.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:51.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:57.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    3.61
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    3.02
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:12.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:38.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.18
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.10
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.13
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.86
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.96
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.52
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.69
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.06
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.39
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:02.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6884.21
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.60
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.46
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:06.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.30
p-value of test                       :    0.9977


-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.27
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5100.33
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:13.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908339
  j =  2                              :            45826
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908480
  j =  2                              :            45751
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:29.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:19.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:01.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:54.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:33.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.83e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.11e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 5.18e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:38.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 4.35e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.00
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.80
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.77
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.55
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.85
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.07
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:39.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.31
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17635.14
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:54.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.85
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.28
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.27
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.60
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.33
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.14
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.76
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.68
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.19
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.63
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  417.00
p-value of test                       :    0.9971


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.25
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.65
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.03
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  427.27
p-value of test                       :    0.9918


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.54
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   36.06
p-value of test                       : 1 -  5.9e-5    *****


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.55
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.03
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.80
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  151.41
p-value of test                       :    0.9957


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.69
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.06
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.00
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.70
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.71
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.58
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:19.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.24
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:21.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 6.10e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.93e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.63
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.62
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:07.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:07.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10201.53
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9786.35
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.67
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:41.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5042.26
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4777.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:50.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4008.16
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.92
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11989.72
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11801.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.88
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999970028

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.83
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999933356

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.03
p-value of test                       :    0.02

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    2.98
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:14.98
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 C (L=1000, r=20)   1 -  5.9e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 103940119.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:40.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:51.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997229
  j =  2                              :             1384
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1259
p-value of test                       :    0.9979

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334379
  j =  1                              :        599997482
  j =  2                              :             1259
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1474
p-value of test                       :  1.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334594
  j =  1                              :        599997052
  j =  2                              :             1474
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5483
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:47.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:38.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:38.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:02.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:02.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:50.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:58.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.95
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    3.58
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     847
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    2.33
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.30
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    4.52
p-value of test                       :  4.9e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     269
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:13.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    2.00
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.92
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.87
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.34
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.48
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.95
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.15
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.87
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:45.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1578.77
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:02:02.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6982.68
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.69
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.51
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:05.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.04
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.38
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:32.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5067.98
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:14.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46207
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870207
  j =  1                              :        399907588
  j =  2                              :            46203
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45694
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869694
  j =  1                              :        399908615
  j =  2                              :            45688
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:27.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:19.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:00.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:33.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 3.44e-4
p-value of test                       :  8.9e-3

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.71e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.59
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.60
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   72.21
p-value of test                       :  4.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.12
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:39.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-3
p-value of test                       :    0.9982

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   64.34
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.73
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.59
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.31
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17348.75
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.00
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.18
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.43
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.14
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.17
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.81
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.83
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.14
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.83
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.77
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.74
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.01
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.41
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.07
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.06
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.31
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.39
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.44
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.67
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.34
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.82
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.26
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.04
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.92
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:34.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.26
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.25
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.63
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.36
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.04
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.62
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:19.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.62
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:20.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:11.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 3.77e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:46.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.01e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.89
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.08
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.91
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:07.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:07.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10185.55
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.40
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:46.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.28
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:51.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.68
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3985.35
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11729.12
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11597.39
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:31.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.58
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000138913

Normal statistic for number of bits   :    1.10
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.59
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000020332

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    5.28
p-value of test                       :  2.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -3.10
p-value of test                       :    0.9990    *****

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:08.57
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 64  WeightDistrib, r = 26           4.7e-4
 105  AutoCor, d=1, r=27              0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 104857623.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1261
p-value of test                       :    0.9975

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334381
  j =  1                              :        599997478
  j =  2                              :             1261
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:54.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:41.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4465
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:02.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:01.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:53.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:55.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.75
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    2.17
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:12.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    3.59
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.59
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.55
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.57
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.41
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.55
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.74
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.58
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  388.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:47.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1507.16
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:09.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6893.80
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.40
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.14
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:09.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.06
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.11
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5007.04
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:13.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45751
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869751
  j =  1                              :        399908504
  j =  2                              :            45739
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45529
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869529
  j =  1                              :        399908944
  j =  2                              :            45525
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:29.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:20.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:02.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:36.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.71e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.29e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:45.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.56
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.26
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.63
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-3
p-value of test                       :    0.9979

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17502.58
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.56
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.69
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.51
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.77
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.94
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.99
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   45.54
p-value of test                       :  5.0e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.61
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.91
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.16
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.76
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.31
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.10
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.35
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.03
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  444.78
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.56
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.17
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.31
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.76
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4899.77
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.03
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.18
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.70
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.52
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4799.18
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.70
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.83
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.44
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:24.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.35
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.33e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.12
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.44
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.10
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:05.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9846.16
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10106.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.038
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:04:25.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4779.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:53.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.4e-3

Kolmogorov-Smirnov- statistic = D-    : 6.83e-3
p-value of test                       :    0.9927

Anderson-Darling statistic = A2       :    4.39
p-value of test                       :  5.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4607.74
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:01:53.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4301.34
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11716.27
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:31.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11947.29
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:31.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.06
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999966908

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.54
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999922025

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.081
p-value of test                       :    0.47

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:15.96

 All tests were passed




Server wird beendet - Lösche Semaphor 105873431.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5345
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:54.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7488
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:38.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:02.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:01.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:51.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:59.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    3.66
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     950
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:11.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:40.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.90
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.14
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.32
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.38
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.26
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.42
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1336.11
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:00.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6786.91
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.34
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:02.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.84
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.42
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5137.39
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:00.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46033
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870033
  j =  1                              :        399907939
  j =  2                              :            46023
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46229
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870229
  j =  1                              :        399907549
  j =  2                              :            46215
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:27.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:20.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:02.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:55.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:35.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:48.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.07
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.47
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.01
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.70
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:37.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.76
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.99
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.00
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17161.65
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.49
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.11
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.93
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.52
p-value of test                       :    0.9921


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.76
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.67
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.94
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.34
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.05
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.47
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.59
p-value of test                       :    0.9911


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.31
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.66
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.21
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.57
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.68
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.14
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.10
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.85
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.06
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.37
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.03
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.91
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.62
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.76
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.38
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.74
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.50
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.62
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    2.40
p-value of test                       :  8.2e-3



-----------------------------------------------
CPU time used                    :  00:02:23.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.55
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:23.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.01e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 4.84e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.47
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.56
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.37
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:04.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.19
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.69
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9870.27
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:42.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:49.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4814.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:50.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4231.98
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.04
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11793.01
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11936.66
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.31
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000015223

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.39
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000151864

Normal statistic for number of bits   :    1.20
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9918

Tests on the sum of all N observations
Standardized normal statistic         :  -0.077
p-value of test                       :    0.53

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:08.29

 All tests were passed




Server wird beendet - Lösche Semaphor 106954775.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5380
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:55.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4127
p-value of test                       :    0.9993    *****


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:01.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:01.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7174
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:52.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7486
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:58.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.90
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.65
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:11.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.17
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    3.50
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    2.10
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:39.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.20
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.28
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.09
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.94
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.83
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.91
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.18
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.33
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1515.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:59.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6947.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.56
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:02.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.31
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.94
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:33.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5204.76
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:59.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45764
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869764
  j =  1                              :        399908474
  j =  2                              :            45760
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46002
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870002
  j =  1                              :        399908001
  j =  2                              :            45992
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:27.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:18.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:45.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.36e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:36.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.63
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:47.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.92
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.80
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   48.15
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:36.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.53
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.27
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17477.28
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.37
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.05
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.07
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.10
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.57
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.12
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.11
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.67
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.17
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.48
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.17
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.75
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.43
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.69
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.96
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.96
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.18
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.16
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.33
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.79
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.03
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.93
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.81
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.22
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5100.37
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.40
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.84
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.13
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   0.083
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:24.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.98
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:23.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    0.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.17e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 9.30e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.27e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 7.66e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.71
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.36
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:02.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:05.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9912.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9934.76
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:51.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.38
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:50.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4795.33
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.47
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.98
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11953.11
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12002.41
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.35
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999947195

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   83.18
p-value of test                       :  6.6e-3


-----------------------------------------------
Total number of bits:  7999841880

Normal statistic for number of bits   :   -1.25
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:08.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 14  BirthdaySpacings, t = 3         0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 107937815.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5437
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:56.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4220
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:55.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:02.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:01.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:53.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:00.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:45.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.59
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    3.03
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:10.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.12
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.11
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.82
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  189.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.60
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:44.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.60
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:59.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6987.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.43
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:02.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.11
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.46
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:35.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5284.33
p-value of test                       :  7.9e-3


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:00.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46009
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870009
  j =  1                              :        399907987
  j =  2                              :            45999
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45629
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869629
  j =  1                              :        399908748
  j =  2                              :            45617
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:28.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:20.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
p-value of test                       :    0.9908

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  4.9e-3

Anderson-Darling statistic = A2       :    4.27
p-value of test                       :  6.6e-3


-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:03.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:54.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.11
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:47.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.65
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.27
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.20
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.03
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:36.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.93
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.70
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17402.48
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.17
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.37
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.37
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.12
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.85
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.36
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.64
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.64
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.01
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.40
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.88
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.89
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.85
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.30
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.91
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.06
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.59
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.97
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.81
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.19
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.03
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.50
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.63
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.41
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.82
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.84
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.57
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.45
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.93
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:22.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.08
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:21.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.22
p-value of test                       :    0.99

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.96
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.85
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.37
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:03.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.26
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:06.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10210.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10169.13
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:43.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5101.75
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4770.67
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.59
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.24
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12036.26
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11950.65
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:30.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.74
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000064276

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.73
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999905111

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.21
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:02.62

 All tests were passed




Server wird beendet - Lösche Semaphor 108920855.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1470
p-value of test                       :  2.4e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334590
  j =  1                              :        599997060
  j =  2                              :             1470
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5522
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:56.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7154
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:04.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:03.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:55.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7152
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:59.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.52
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:11.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    2.30
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.76
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.57
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.03
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.05
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.20
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.94
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  195.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.10
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.25
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7132.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.81
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:04.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.86
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.66
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:30.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4956.25
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:15.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45911
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869911
  j =  1                              :        399908181
  j =  2                              :            45905
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46083
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870083
  j =  1                              :        399907837
  j =  2                              :            46077
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:19.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:45.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:01.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:54.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 3.01e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.51
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:01:36.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.84
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.92
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.03
p-value of test                       :    0.9900

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.32
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:37.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.83
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.51
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17608.51
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.19
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.49
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.21
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.57
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.99
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.42
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.57
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.46
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.18
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.34
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.87
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.06
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.24
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.88
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.77
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.28
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.75
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.59
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.42
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.53
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.75
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.11
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.43
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.82
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.94
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.38
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.76
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5135.45
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.77
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.13
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.23
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:22.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.61
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -1.48
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:23.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.10e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 9.22e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.62e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.76
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.63
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   40.00
p-value of test                       :  4.5e-3



-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:04.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.13
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.15
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10198.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.054
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.083
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.023
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:42.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5050.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:50.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4716.38
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:53.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.83
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:31.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12014.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:32.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.15
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000077509

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.56
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999981866

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:37.17

 All tests were passed




Server wird beendet - Lösche Semaphor 109936663.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5250
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:56.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:04.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:53.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:59.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    2.27
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     646
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:13.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:38.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.48
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.01
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.17
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.60
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.82
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.60
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1546.63
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.53
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.94
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:04.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.77
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.77
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.39
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:11.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45592
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869592
  j =  1                              :        399908817
  j =  2                              :            45590
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45931
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869931
  j =  1                              :        399908141
  j =  2                              :            45925
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:28.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:19.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:54.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.69e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.92e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.056
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.071
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:35.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.86
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.39
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.59
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.06
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.82
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:39.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.15
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.20
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.59
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17753.20
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.25
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.39
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.81
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.44
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.18
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.39
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.20
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.52
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.70
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.91
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.64
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.37
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.37
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.49
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.48
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.22
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.33
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.13
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.80
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.39
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.17
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.58
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.69
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.82
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.10
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.96
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.06
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.32
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.91
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.57
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.38
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:21.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.15
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:21.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 5.56e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.36e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.62
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.72
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:05.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.09
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9783.88
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9867.40
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:39.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.86
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:49.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.55
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4025.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11665.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.22
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999997457

Normal statistic for number of bits   :  -0.020
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.35
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000108265

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.84
p-value of test                       :    0.03

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:29.62

 All tests were passed




Server wird beendet - Lösche Semaphor 110886935.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5332
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:58.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:42.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4477
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:59.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:07.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:06.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:57.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:59.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    2.22
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     849
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.06
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     263
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:13.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.37
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.59
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.54
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.89
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.27
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.40
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.34
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:46.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.89
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:06.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7021.85
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.98
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:08.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.75
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.98
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5070.36
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:59.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45679
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869679
  j =  1                              :        399908645
  j =  2                              :            45673
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45937
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869937
  j =  1                              :        399908128
  j =  2                              :            45933
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:29.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:18.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  8.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:02.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 9.19e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:44.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.034
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.71
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.97
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.78
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.86
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17201.06
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.43
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.94
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.02
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.67
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.08
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.31
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.65
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.76
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.70
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.39
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.41
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.52
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.99
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.44
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.87
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.87
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.09
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.21
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.21
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.05
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.13
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.94
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5138.22
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.61
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:34.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.14
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.79
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.49
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.92
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.02
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:34.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.25
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :   -1.39
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:22.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.60
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:21.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.53e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.36
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.22
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.78
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:04.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.81
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:05.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9918.81
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10109.69
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:04:18.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:10.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5060.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:08.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.81
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.89
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.66
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11772.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:40.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.93
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  7999986564

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.03
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000045751

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.88

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:24.76

 All tests were passed




Server wird beendet - Lösche Semaphor 111837207.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5360
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:56.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:41.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4210
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7513
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:04.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:03.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:54.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:59.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:11.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.27
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:39.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.72
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.43
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.99
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.06
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.08
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1520.51
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:00.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6931.01
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.95
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.04
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:04.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.12
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.93
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:34.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5017.64
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:04.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45688
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869688
  j =  1                              :        399908627
  j =  2                              :            45682
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46007
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870007
  j =  1                              :        399907989
  j =  2                              :            46001
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:27.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:19.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:53.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:32.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 9.71e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.084
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:40.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.59
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.87
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.16
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:38.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.85
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.41
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   15.29
p-value of test                       :  4.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.69
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17399.82
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:52.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.75
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.41
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.06
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.52
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.53
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.88
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.51
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.31
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.92
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.43
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.51
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.18
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.76
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.62
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.48
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.60
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.29
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.45
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.72
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.62
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.00
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.96
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5080.37
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.46
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.93
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.25
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.31
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.80
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.70
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.95
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.53
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:22.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.45
p-value of test                       :    0.9915


-----------------------------------------------
Normal statistic for number of jumps  :   0.070
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:23.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.04
p-value of test                       :    0.02

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.42e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 6.50e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.76
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.58
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:04.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.14
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:04.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9963.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:42.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4795.80
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.03
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4294.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.09
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11609.27
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11978.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.84
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999971741

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.81
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000038044

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:36.68
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 70  MatrixRank, L=5000              4.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 112918551.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5525
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:58.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:43.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:46.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:02.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7150
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:09.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:11.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.64
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     333
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:11.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:41.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.80
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.69
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.61
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.72
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.22
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.75
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:08.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7173.61
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.53
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:18.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.17
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.43
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:44.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5022.34
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:58.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45718
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869718
  j =  1                              :        399908567
  j =  2                              :            45712
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45620
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869620
  j =  1                              :        399908763
  j =  2                              :            45614
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:32.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:20.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:54.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:11.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:57.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:39.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:53.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.22
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.33
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.43
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.34
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.67
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:54.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.55
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.95
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.00
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17425.87
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.71
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.39
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.77
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.05
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.83
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.21
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.66
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.15
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.01
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.48
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.83
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.35
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.96
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.29
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.37
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.87
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.82
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.82
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.78
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.89
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.40
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.65
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.32
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.86
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.01
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.09
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.21
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.83
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.98
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -1.28
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:22.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.31
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:23.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 4.61e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.40e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.86
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.47
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.34
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:05.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.20
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10278.52
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.084
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:04:32.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.70
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:52.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5043.04
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.80
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4012.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.80
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:33.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11765.52
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:37.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.00
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000065269

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.85
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999945254

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:36.27

 All tests were passed




Server wird beendet - Lösche Semaphor 113934359.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5344
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:55.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:03.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:04.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:54.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:59.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:44.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:11.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    2.07
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:43.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.78
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.37
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.25
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.55
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.54
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.92
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.18
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.25
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1387.70
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:01.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6888.17
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.41
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:02.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.28
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.46
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5032.41
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:58.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45780
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869780
  j =  1                              :        399908447
  j =  2                              :            45766
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45406
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869406
  j =  1                              :        399909191
  j =  2                              :            45400
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:27.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:33.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.32e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.36
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.69
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:47.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.21
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.14
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.61
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:38.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.37
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.23
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17327.72
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.28
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.19
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.32
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.05
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.57
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.42
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.95
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.54
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.00
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.91
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.81
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.06
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.14
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.44
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.75
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.60
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.28
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.08
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.05
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.86
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.64
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.62
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.93
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.94
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.28
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.46
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.85
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.02
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:34.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.27
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:22.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.62
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :    1.94
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:22.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.97

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.14e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.57e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.79
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.96
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  1.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.91
p-value of test                       :  3.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9593.05
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9796.79
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:43.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    4.86
p-value of test                       :  3.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4611.77
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.92
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.12
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11659.31
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11917.64
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.18
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999989951

Normal statistic for number of bits   :  -0.079
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.19
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000101962

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.05

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:14.20

 All tests were passed




Server wird beendet - Lösche Semaphor 115212311.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5442
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:55.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:40.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:05.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7468
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:58.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7172
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:01.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    3.98
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.15
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     267
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:14.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:42.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.06
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.13
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.53
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.44
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.68
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.73
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.79
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  191.42
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1483.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:08.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7100.26
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.40
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.74
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.83
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:38.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5119.18
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:04.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45949
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869949
  j =  1                              :        399908102
  j =  2                              :            45949
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45599
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869599
  j =  1                              :        399908805
  j =  2                              :            45593
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:24.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:29.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:03.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.96e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.15e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.066
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.13
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.77
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.57
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.74
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.20
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.63
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.97
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.79
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17372.83
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.73
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.79
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.61
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.84
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.69
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.03
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.26
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.53
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.56
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.28
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.65
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.27
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.02
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.31
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.07
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.78
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  593.03
p-value of test                       :  2.6e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.73
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.90
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.53
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.59
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.15
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.18
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.48
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.60
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.99
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4885.91
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.44
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.33
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.88
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -1.95
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:23.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.82
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:25.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.86e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 8.67e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.63e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.62
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.17
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.46
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:08.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:08.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9934.21
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10219.06
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:04:17.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.16e-3
p-value of test                       :    0.9967

Anderson-Darling statistic = A2       :    4.73
p-value of test                       :  4.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4589.17
p-value of test                       :    0.9990    *****

-----------------------------------------------
CPU time used                    :  00:01:52.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.48
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:31.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:31.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.52
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000127780

Normal statistic for number of bits   :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.56
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000078313

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    5.10
p-value of test                       :  2.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -3.10
p-value of test                       :    0.9990    *****

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:37.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 95  HammingIndep, L=30, r=0         0.9990 
 103  AutoCor, d=1, r=0               0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 116162583.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5322
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:53.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:40.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:40.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:05.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:57.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7105
p-value of test                       :    0.9938


-----------------------------------------------
CPU time used                    :  00:03:59.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:45.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    4.64
p-value of test                       :  4.3e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     548
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:12.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.66
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.08
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.50
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.53
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.82
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.89
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.15
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:04.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7132.79
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.82
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:09.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.93
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.84
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:37.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.44
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:54.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45739
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869739
  j =  1                              :        399908525
  j =  2                              :            45733
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45718
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869718
  j =  1                              :        399908567
  j =  2                              :            45712
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:28.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:18.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:05.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:57.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.22e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 3.16e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.43
p-value of test                       :  5.4e-3

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.67
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.01
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.36
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.82
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.63
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.36
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.01e-3
p-value of test                       :    0.9990

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17195.77
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.79
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.68
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.84
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.45
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.16
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.12
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.83
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.44
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.38
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.54
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.20
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.44
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.26
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.44
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.01
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.11
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.46
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.95
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   97.43
p-value of test                       :    0.9948


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.91
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.43
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.34
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.06
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.25
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.83
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.77
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.50
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4794.40
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.73
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.33
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.24
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:22.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.83
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -1.71
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 5.82e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 2.70e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.10
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.95
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.14
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:06.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.70
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:06.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10116.14
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9845.34
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:04:15.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5036.72
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:52.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4999.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:54.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4285.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.61
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11921.76
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11759.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.46
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999988097

Normal statistic for number of bits   :  -0.094
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.30
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999918014

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.1e-3

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:37.30

 All tests were passed




Server wird beendet - Lösche Semaphor 117145623.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5473
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:53.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:39.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:39.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:05.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:56.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:57.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.73
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:12.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.72
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.27
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.00
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.58
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.08
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.55
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.53
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.37
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.38
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.93
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.42
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:06.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7234.88
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.56
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.97
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:09.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.12
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.49
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:38.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4910.13
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:54.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45757
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869757
  j =  1                              :        399908488
  j =  2                              :            45753
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45852
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869852
  j =  1                              :        399908297
  j =  2                              :            45850
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:30.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:19.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:06.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:04.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.46e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-5
p-value of test                       :    0.9939

Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.96
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.50
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.28
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.86
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.03
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.90
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.62
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17472.36
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.42
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.27
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.37
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.55
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.41
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.41
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.42
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.51
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.88
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.70
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.70
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.77
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.38
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.90
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.06
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.14
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.74
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.42
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.88
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.07
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.62
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5144.27
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.95
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.08
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.10
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.13
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.18
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.80
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.66
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.66
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:25.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.95
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:23.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 6.72e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.57
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.94
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.33
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:05.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.74
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:04.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10165.51
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9951.21
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:04:12.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4766.59
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:53.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.33
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:54.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.01
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4316.63
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11725.15
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.28
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:31.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.11
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  7999877631

Normal statistic for number of bits   :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.32
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000001978

Normal statistic for number of bits   :   0.016
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:10.85

 All tests were passed




Server wird beendet - Lösche Semaphor 118259735.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:53.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4232
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:04.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:03.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:53.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:00.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:47.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:12.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:44.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.52
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.11
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.49
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.22
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.61
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.81
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.04
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.99
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.54
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.88
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:01.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6893.00
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:41.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.58
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:00.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.37
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.24
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:35.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.99
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:57.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46300
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870300
  j =  1                              :        399907410
  j =  2                              :            46280
  j =  3                              :               10
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45568
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869568
  j =  1                              :        399908868
  j =  2                              :            45560
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:29.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:19.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:45.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:02.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  8.5e-3

Anderson-Darling statistic = A2       :    3.52
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.35e-3
p-value of test                       :    0.9928

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:33.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.58e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 7.83e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 2.92e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:35.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.058
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.10
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:48.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.03
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.14
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.34
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.76
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.12
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.66
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.31
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.52
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17416.97
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.37
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.37
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.38
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.43
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.72
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.85
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.04
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.21
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.63
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  444.51
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.98
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.43
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.13
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.61
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.09
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.49
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.87
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.64
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.02
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5069.00
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.20
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.74
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.04
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  469.33
p-value of test                       :  1.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4909.81
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.50
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  156.34
p-value of test                       :    0.9901


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.67
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    2.45
p-value of test                       :  7.2e-3



-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.32
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.47e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 8.51e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.61e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 9.42e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.42
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   21.21
p-value of test                       :  6.6e-3

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:05.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9839.81
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.94
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.18
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:40.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5004.21
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.53
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.37
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11934.02
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11687.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.89
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000073474

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.99
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999904835

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.93
p-value of test                       :    0.97

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.32

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         : -6.20e-4
p-value of test                       :    0.50

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:10.69

 All tests were passed




Server wird beendet - Lösche Semaphor 119308311.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:54.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4194
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:03.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:03.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:54.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:59.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:45.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.76
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    2.72
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:13.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.10
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:38.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.56
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.72
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.58
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.02
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.53
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.64
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.63
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.86
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.79
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:44.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.75
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:02.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6795.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:41.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.83
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.91
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:04.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.97
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.70
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:33.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4923.74
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:55.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45726
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869726
  j =  1                              :        399908549
  j =  2                              :            45724
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46126
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870126
  j =  1                              :        399907750
  j =  2                              :            46122
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:27.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:18.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:59.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:33.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 9.27e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:37.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.52
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.16
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:47.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.68
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.77
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.85
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:38.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.30
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.80
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.72
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.07
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17388.33
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.34
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.11
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.96
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.57
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.83
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.22
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.77
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.51
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.55
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.36
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.47
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.68
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.98
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.30
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.03
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.70
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.44
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.46
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.52
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.19
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.10
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.51
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.39
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.36
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  322.91
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4893.58
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.68
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.57
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.44
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:22.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.72
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -1.90
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:22.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.09e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.57
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.19
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9962

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:04.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:07.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9838.67
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.031
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:42.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.90
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.87
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:49.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.98
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.26
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11541.07
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.55
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999991079

Normal statistic for number of bits   :  -0.071
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.52
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999950423

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.5e-3

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.12
p-value of test                       :    0.02

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:01.87

 All tests were passed




Server wird beendet - Lösche Semaphor 120225815.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:56.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:40.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:54.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:59.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    2.15
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     944
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    4.01
p-value of test                       :  8.6e-3

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    2.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:11.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.66
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.09
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.16
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.16
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.14
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.91
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:44.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.95
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6741.87
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.94
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:02.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.80
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.22
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:35.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5027.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:58.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45722
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869722
  j =  1                              :        399908557
  j =  2                              :            45720
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46016
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870016
  j =  1                              :        399907969
  j =  2                              :            46014
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:27.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:19.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:33.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.20e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.10e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.52e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.54
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.17
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.04
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.65
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.64
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9971

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.46
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17498.96
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.89
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.21
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.92
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.07
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.31
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.50
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.15
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   37.30
p-value of test                       :  3.1e-3


-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.95
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.08
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  582.00
p-value of test                       :  6.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.66
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.39
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.32
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.80
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   99.53
p-value of test                       :    0.9919


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.50
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.50
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5344.65
p-value of test                       :  3.7e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.20
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.66
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.59
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.50
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5147.25
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.81
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.39
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.69
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:23.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.58
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:23.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 5.65e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:46.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 7.76e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.63
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.99
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.92e-3
p-value of test                       :    0.9959

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  244.74
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.48
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.93
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9956.60
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.098
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:30.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5001.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:44.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.0e-3

Kolmogorov-Smirnov- statistic = D-    : 3.05e-3
p-value of test                       :    0.9969

Anderson-Darling statistic = A2       :    7.02
p-value of test                       :  3.6e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4536.83
p-value of test                       :    0.9999    *****

-----------------------------------------------
CPU time used                    :  00:01:43.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.77
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.26
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12230.92
p-value of test                       :  4.5e-3

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.80
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000033094

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.25
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999889535

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:00:23.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 J (L=10000, r=0)    3.7e-4
 96  HammingIndep, L=30, r=27        0.9999 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 121307159.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5469
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:41.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:36.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:34.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:54.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:02.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:01.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:55.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7475
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:00.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    4.28
p-value of test                       :  6.3e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     955
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:51.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.02
p-value of test                       :  2.9e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:10.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:34.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.90
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.48
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.09
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.38
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1406.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7304.75
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:45.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.28
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:02.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.28
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.36
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:36.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4982.97
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:10.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45972
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869972
  j =  1                              :        399908056
  j =  2                              :            45972
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46070
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870070
  j =  1                              :        399907867
  j =  2                              :            46056
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:28.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:17.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:44.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:51.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 9.40e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.26e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.026
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:38.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.15
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.22
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.34
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.74
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.69
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.47
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.85
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.79
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:32.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:31.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.76
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17246.91
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.71
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.29
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.66
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.37
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.30
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.66
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.22
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.90
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.71
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.32
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:40.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.20
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.21
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.05
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.46
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.14
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:47.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.44
p-value of test                       :    0.9914


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.67
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.06
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.42
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.82
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.20
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.99
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.90
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.65
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.09
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.53
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.37
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  447.71
p-value of test                       :  7.8e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.54
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.64
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :  -0.086
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:14.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.36
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :    1.78
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:12.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.04e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.57e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 9.48e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.78
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.48
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.78
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:10.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.98
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:12.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9765.78
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10025.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:44.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.74
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:48.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.06
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.60
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.02
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11660.90
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11663.52
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.75
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999983852

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.73
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999995678

Normal statistic for number of bits   :  -0.034
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:29.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:28.64

 All tests were passed




Server wird beendet - Lösche Semaphor 102367256.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1239
p-value of test                       :    0.9997    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334359
  j =  1                              :        599997522
  j =  2                              :             1239
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5308
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:44.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:37.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:35.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4225
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:53.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7132
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:01.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:02.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:54.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:58.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     950
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.37
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     272
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:12.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.89
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    2.89
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     126
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:50.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.68
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.76
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.02
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.97
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.14
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.32
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.87
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1488.46
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7374.44
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:50.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:10.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.96
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.46
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:38.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.61
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:22.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46074
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870074
  j =  1                              :        399907852
  j =  2                              :            46074
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45516
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869516
  j =  1                              :        399908972
  j =  2                              :            45508
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:30.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:19.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:43.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:54.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:36.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.19e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 3.59e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -3.06
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.23
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.92
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.58
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.83
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.68
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17264.09
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.18
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.55
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.62
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.15
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.81
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.52
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.50
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.88
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.52
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.87
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.97
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.83
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.02
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.89
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.93
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.55
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.45
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.57
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.62
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.57
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.76
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.85
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.09
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.92
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.69
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.24
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5225.37
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.89
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.54
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.60
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:24.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.90
p-value of test                       :    0.9962


-----------------------------------------------
Normal statistic for number of jumps  :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:26.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.14e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 9.29e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.90
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.01
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.77
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:08.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.26
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:07.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9773.49
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9801.00
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.034
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:04:19.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.65
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:52.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5031.97
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.36
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4194.62
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.65
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:34.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12070.49
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:31.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.33
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000109015

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.00
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999956993

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:11.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 103120920.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5274
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:48.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:38.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:36.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:54.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:02.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:03.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:55.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:03.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.22
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9925

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    3.73
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:12.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    3.19
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     127
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:46.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.34
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.54
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.38
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.19
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.17
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.25
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1327.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:06.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6961.03
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.90
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:14.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.72
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.70
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5153.45
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:00.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45920
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869920
  j =  1                              :        399908162
  j =  2                              :            45916
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45780
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869780
  j =  1                              :        399908441
  j =  2                              :            45778
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:27.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:15.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:35.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.73
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.38
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.80
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.69
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17336.30
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.32
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.71
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.60
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.02
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.70
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.60
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.69
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.70
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.55
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.77
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.74
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.95
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.92
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.08
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.92
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.44
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.49
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.68
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.32
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.92
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.69
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.83
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.39
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.80
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.43
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.81
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.63
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4853.15
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.15
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.35
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.87
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   0.066
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:25.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.16
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    1.67
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:24.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   0.033
p-value of test                       :    0.49

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.35e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 8.00e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.56
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.56
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:09.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-3
p-value of test                       :    0.9981

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.22
p-value of test                       :  7.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  265.05
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:02:09.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.80
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.098
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:04:22.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.94
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.73
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:55.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.97
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:31.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11575.45
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:31.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.16
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999939149

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.07
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000024409

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   0.039
p-value of test                       :    0.48

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:16.54

 All tests were passed




Server wird beendet - Lösche Semaphor 104300568.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:55.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5499
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:49.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:38.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:06.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:08.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:07.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:12.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9904

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:14.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.26
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.71
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.88
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.85
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.85
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.09
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1509.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6933.46
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.30
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.68
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:19.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.96
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.21
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4992.65
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:02.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45960
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869960
  j =  1                              :        399908083
  j =  2                              :            45954
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45548
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869548
  j =  1                              :        399908907
  j =  2                              :            45542
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:32.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:18.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.8e-3

Kolmogorov-Smirnov- statistic = D-    : 1.02e-3
p-value of test                       :    0.9990

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9961


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:04.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.66e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.10
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.66
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.17
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.33
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.85
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:11.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.05
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.58
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.84
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17594.09
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.24
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.79
p-value of test                       :    0.9939


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.45
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.94
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.61
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.75
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   47.68
p-value of test                       :  4.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.58
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.28
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.79
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.25
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.94
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.31
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.25
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.41
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.96
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.64
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.66
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.40
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.02
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.25
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.93
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.76
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.53
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.52
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.18
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5081.50
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.90
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  240.76
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.75
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.60
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:25.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.17e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.60
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.29
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.13
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:06.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.64
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:07.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.68
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10073.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:04:26.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.28
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:55.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:00.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.14
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.58
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11789.28
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:33.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11811.81
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:35.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.65
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999956762

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.94
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999966665

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:32.39

 All tests were passed




Server wird beendet - Lösche Semaphor 105349144.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:51.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997327
  j =  2                              :             1335
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1484
p-value of test                       :  7.2e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334604
  j =  1                              :        599997032
  j =  2                              :             1484
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:51.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7462
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:05.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:04.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:55.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:00.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    2.39
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:03.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.51
p-value of test                       :  5.2e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:13.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    3.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:42.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.30
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.72
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.78
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.92
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  496.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:43.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1346.91
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:02.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7051.99
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.08
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:04.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.34
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.57
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5067.97
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  1.9e-4    *****


-----------------------------------------------
CPU time used                    :  00:02:56.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45983
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869983
  j =  1                              :        399908040
  j =  2                              :            45971
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46090
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870090
  j =  1                              :        399907822
  j =  2                              :            46086
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:27.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.69e-3
p-value of test                       :    0.9946

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9956


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:18.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:45.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:01.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.82e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.58e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:35.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.36
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.00
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.80
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   33.95
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.68
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.72
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.14
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17153.66
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.44
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.71
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.52
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.95
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.22
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.67
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.35
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.54
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.11
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.58
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.92
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.34
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.90
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.87
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.01
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.08
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  440.37
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.16
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.29
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.80
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.89
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4875.94
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.71
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.15
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  457.61
p-value of test                       :  5.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.10
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.67
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.40
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.17
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:25.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.44
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -1.54
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:25.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9939

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.46e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 4.49e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.84e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.48
p-value of test                       :    0.9931

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.31
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.77
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.68
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:06.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.19
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.10
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:04:25.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.83
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4786.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4007.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3960.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11948.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11578.96
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.35
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999934475

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.17
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999970661

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.06
p-value of test                       :    0.02

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:10.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14           7.2e-4
 43  Permutation, t = 10             1.9e-4
 61  WeightDistrib, r = 28           0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 106430488.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5496
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:52.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:40.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4469
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:57.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:07.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:06.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:00.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:03.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:13.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    3.05
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.94
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.65
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.98
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.27
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.57
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.08
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:50.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1492.35
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:02.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6800.69
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.48
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.44
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:09.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.94
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.19
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4943.06
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:00.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45781
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869781
  j =  1                              :        399908440
  j =  2                              :            45777
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45931
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869931
  j =  1                              :        399908140
  j =  2                              :            45927
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:29.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:18.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:03.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.13e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.10e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.86
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.46
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.70
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.98
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.04
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.68
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.34
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.37
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17512.84
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.96
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.15
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.91
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.65
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.99
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.96
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.90
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.87
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.05
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   35.76
p-value of test                       :  4.9e-3


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.17
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.71
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.11
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.09
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.90
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.27
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.64
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.87
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.84
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.20
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.21
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.67
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.06
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.74
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.75
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.88
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.45
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.27
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.15
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.05
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.47
p-value of test                       :  6.6e-3


-----------------------------------------------
Normal statistic for number of jumps  :   -1.20
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:23.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.90
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:25.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.41e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.24e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.67
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.74
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.90
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:06.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.71
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:06.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.60
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.53
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:04:15.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.53
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:51.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:52.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4259.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.84
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11895.38
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12030.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.42
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000013966

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.08
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999952940

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.23

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:48.64

 All tests were passed




Server wird beendet - Lösche Semaphor 107380760.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5552
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:51.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:40.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4216
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:57.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:05.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:55.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:01.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.63
p-value of test                       :  1.5e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:13.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:43.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.99
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.80
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.75
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.04
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1381.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:02.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7033.04
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:41.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    4.04
p-value of test                       :  8.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.37
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:02.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.74
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.58
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5086.94
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:57.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45614
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869614
  j =  1                              :        399908777
  j =  2                              :            45604
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46130
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870130
  j =  1                              :        399907744
  j =  2                              :            46122
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:28.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:18.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:45.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:01.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.80e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:35.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.47
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.87
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.43
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.13
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.62
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.01
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.11
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17494.40
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.19
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.12
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.78
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.98
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.63
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.02
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.16
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.54
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.57
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.28
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.19
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.25
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  182.51
p-value of test                       :  4.8e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.32
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.93
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.09
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.74
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.63
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.63
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.52
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.11
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.57
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.70
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.81
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.21
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.95
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4899.64
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.35
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.94
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    2.12
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:22.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.36
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:23.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.55e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.75e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.14
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.25
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.85
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.52
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:07.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9790.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.38
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:42.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.80
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.89
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4237.75
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.68
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.58
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11661.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.78
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999926861

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.29
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999894419

Normal statistic for number of bits   :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:49.79

 All tests were passed




Server wird beendet - Lösche Semaphor 108560408.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:50.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:39.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:40.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4204
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:06.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:06.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:56.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7120
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:04:03.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:15.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    2.71
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.71
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.69
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.32
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.53
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.87
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:02.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6936.25
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:41.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.69
p-value of test                       :  3.4e-3

Anderson-Darling statistic = A2       :    6.78
p-value of test                       :  4.9e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   62.03
p-value of test                       :  5.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:05.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.24
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.85
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5109.46
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:55.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45851
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869851
  j =  1                              :        399908301
  j =  2                              :            45845
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46027
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870027
  j =  1                              :        399907949
  j =  2                              :            46021
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:27.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:17.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:54.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:35.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.99e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:37.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.24
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.67
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:48.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.92
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.01
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.6e-3

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.67
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17651.03
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.02
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.97
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.84
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.88
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.11
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.07
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.90
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.30
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.26
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.21
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.46
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.40
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.23
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.71
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.98
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.74
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.58
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.98
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.62
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.07
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.93
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.46
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.75
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.42
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.53
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5069.63
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.30
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.79
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.37
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.48
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:23.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.87e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 8.40e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.64e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.99
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.90
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.73
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:07.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  155.22
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:02:06.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10028.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10009.03
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:43.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.15
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:49.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4261.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.01
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11943.69
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11969.98
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.77
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000067864

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.45
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000068269

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9975

Tests on the sum of all N observations
Standardized normal statistic         :  -0.044
p-value of test                       :    0.52

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:04.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 38  Run, r = 0                      5.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 109477912.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:49.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1469
p-value of test                       :  2.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334589
  j =  1                              :        599997062
  j =  2                              :             1469
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5362
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:50.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7170
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:05.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:55.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:00.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:13.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.64
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.41
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.37
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.91
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.11
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.54
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.77
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.78
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  391.33
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:42.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.71
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:03.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6956.55
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.98
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.22
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:06.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.84
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.31
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5075.39
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:56.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45904
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869904
  j =  1                              :        399908194
  j =  2                              :            45900
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46296
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870296
  j =  1                              :        399907411
  j =  2                              :            46290
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:27.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:54.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 3.96e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.65
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:37.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.00
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.19
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.73
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.44
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.22
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.95
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.48
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.37
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  6.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.93
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17395.22
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.54
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.82
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.30
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.47
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.94
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.32
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.49
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.86
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.16
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.58
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.17
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.56
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.94
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.46
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.83
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.64
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.49
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.35
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.26
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.65
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.74
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4847.52
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.50
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.81
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.08
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.87
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.90
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.62
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.67
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.21
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:25.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.59
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -1.71
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:24.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 6.15e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 9.14e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.21
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.32
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.62
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:06.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.70
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:07.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10161.42
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10043.58
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.087
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:46.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5082.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.59
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:49.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.24
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3993.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11633.52
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11945.70
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.17
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000015583

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.94
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999976991

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-3
p-value of test                       :    0.9988

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:00.13

 All tests were passed




Server wird beendet - Lösche Semaphor 110428184.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5378
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:51.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:38.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:06.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:07.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:58.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:00.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.43
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    3.51
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     333
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:12.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    3.37
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     126
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:44.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.96
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.01
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.82
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.38
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.78
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.88
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.00
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:03.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7014.32
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.37
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.07
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:07.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.53
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:36.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5135.47
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:59.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45860
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869860
  j =  1                              :        399908283
  j =  2                              :            45854
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46286
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870286
  j =  1                              :        399907432
  j =  2                              :            46278
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9946

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:30.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9935


-----------------------------------------------
CPU time used                    :  00:02:19.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:01.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:36.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 8.71e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.082
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.26
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:42.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:44.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.22
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.36
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.45
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   54.19
p-value of test                       :  3.1e-3

-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.17
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.75
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.67
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17818.67
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.33
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.00
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.84
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.24
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.29
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.40
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.69
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.91
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.79
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.36
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.77
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.66
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.10
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.03
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.79
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.98
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.35
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.88
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.08
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.19
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4866.82
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.70
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  159.93
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.86
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.68
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.52
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.42
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.71
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.86
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:24.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.69
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.81e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 6.82e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.98e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 4.72e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.78
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.45
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.25
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:09.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:08.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9701.44
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9803.87
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:04:14.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.28
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:52.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4712.47
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.78
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4203.37
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.15
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:30.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11590.08
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:30.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.66
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999899720

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.00
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000008824

Normal statistic for number of bits   :   0.070
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:07.62

 All tests were passed




Server wird beendet - Lösche Semaphor 111280152.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:50.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:39.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4508
p-value of test                       :  5.0e-3


-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:03.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:55.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:01.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.77
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    3.07
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     848
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    2.42
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     557
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:11.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:42.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.12
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.30
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.67
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.79
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.98
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:02.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7074.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.12
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:05.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.92
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.58
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5108.93
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:53.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45446
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869446
  j =  1                              :        399909112
  j =  2                              :            45438
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908188
  j =  2                              :            45897
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:28.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:18.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  5.4e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:00.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:55.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.78e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:34.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.93
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.97
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.71
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.57
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.64
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.22
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:40.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.93
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.59
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.24
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.90
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17616.50
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.76
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.88
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.27
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.94
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.77
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.28
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.80
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.47
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.03
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.21
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.57
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.09
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.02
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.69
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.89
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.34
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.27
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.43
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.34
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5037.56
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.33
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  264.65
p-value of test                       :  1.5e-3


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.16
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.01
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.05
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.13
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.60
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.58
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -1.30
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:24.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.98
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :  -0.033
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:23.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    2.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.37e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 7.40e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.73e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.81
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.33
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.22
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:08.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.05
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:08.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9853.90
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9734.28
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:49.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4681.93
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:47.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.24
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.40
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.47
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11903.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11629.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.64
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999947867

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.04
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000175900

Normal statistic for number of bits   :    1.39
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:24.20

 All tests were passed




Server wird beendet - Lösche Semaphor 112361496.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:48.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5503
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:51.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:04.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:04.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:55.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:00.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:45.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     642
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:11.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.09
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.97
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.25
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.25
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.68
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.00
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.15
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.95
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1341.07
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:02.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6950.75
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:41.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.76
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:02.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.56
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.24
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4914.58
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:55.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45790
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869790
  j =  1                              :        399908425
  j =  2                              :            45780
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45433
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869433
  j =  1                              :        399909137
  j =  2                              :            45427
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:29.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:18.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:33.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.77e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.91e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.87
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.061
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:35.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.49
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:48.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.61
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.63
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.98
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.26
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.99
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   97.06
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17375.67
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.42
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.00
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   48.20
p-value of test                       :  3.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.31
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.41
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.47
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.70
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.83
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.70
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.56
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.66
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.61
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.42
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.38
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.00
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.34
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.75
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.68
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.06
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.32
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.36
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.52
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.18
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.22
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.14
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.30
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5166.37
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.28
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  255.16
p-value of test                       :  5.1e-3


-----------------------------------------------
CPU time used                    :  00:00:34.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.99
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:22.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.55
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    2.77
p-value of test                       :  2.8e-3



-----------------------------------------------
CPU time used                    :  00:02:22.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.88e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 5.67e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.58
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.64
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  250.40
p-value of test                       :  8.9e-3

-----------------------------------------------
CPU time used                    :  00:02:06.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9940

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:07.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9898.03
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9890.38
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:49.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.95
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:49.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.61
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3992.96
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11734.10
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11934.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.96
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  7999977372

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.65
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999887135

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.08
p-value of test                       :    0.98

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:51.44

 All tests were passed




Server wird beendet - Lösche Semaphor 113279000.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:48.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5591
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:51.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7504
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:38.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:04.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:02.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:55.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7165
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:59.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.96
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.26
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     267
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:12.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.77
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.08
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.10
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.59
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.17
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.60
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7248.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:40.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.65
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:07.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.87
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.16
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4975.91
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:57.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45881
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869881
  j =  1                              :        399908241
  j =  2                              :            45875
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45837
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869837
  j =  1                              :        399908328
  j =  2                              :            45833
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:26.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:16.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.8e-3

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:59.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.98e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.24e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:33.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.23
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:48.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.70
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.33
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.18
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.22
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.02
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.14
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.01
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.23
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.07
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.54e-5
p-value of test                       : 1 -  7.5e-5    *****

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.59
p-value of test                       :  4.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  193.18
p-value of test                       :  2.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.2e-3

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17091.05
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.83
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.14
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.13
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.12
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.43
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.84
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.58
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.84
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.45
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.52
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.36
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.91
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.95
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.43
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.74
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.89
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.91
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.95
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.59
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.40
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.44
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.84
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.34
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.83
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.03
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.06
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.34
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    1.22
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:23.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.02
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.4e-3

Anderson-Darling statistic = A2       :    4.57
p-value of test                       :  4.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.40
p-value of test                       :  8.2e-3

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 8.49e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.74e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 6.61e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.74
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.69
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:06.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.76
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10135.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9790.98
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    3.29
p-value of test                       :  5.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:03:42.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.47
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.82
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4266.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.16
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11368.07
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.89
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  7999984224

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.16
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999785681

Normal statistic for number of bits   :   -1.69
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:02.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 72  Savir2                          2.7e-4
 94  HammingCorr, L = 1200           5.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 114262040.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5464
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:51.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:39.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:57.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:03.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:03.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:54.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:00.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.14
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:12.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    2.16
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:41.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.04
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.64
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.52
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.05
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.60
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  483.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.87
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.50
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.53
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:01.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.66
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:46.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.02
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4983.16
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:53.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46001
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870001
  j =  1                              :        399908000
  j =  2                              :            45997
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46179
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870179
  j =  1                              :        399907648
  j =  2                              :            46167
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:28.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:33.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.18
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.89
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.12
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.05
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:47.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.05
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.41
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.98
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.28
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.64
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.28
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17404.76
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.71
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.81
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.55
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.30
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.03
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.89
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.96
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.93
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.43
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.34
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.83
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.26
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.11
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.84
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.60
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.49
p-value of test                       :    0.9942


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.70
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.26
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.09
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.00
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.21
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.15
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.67
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.88
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.75
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.35
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.18
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4844.07
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.33
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.66
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.71
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:23.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.46
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:23.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :  -0.022
p-value of test                       :    0.51

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.47e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.45e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.56
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.22
p-value of test                       :  9.5e-3

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.00
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:05.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:05.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9756.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10230.70
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:43.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.39
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4695.25
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.72
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.73
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11612.93
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11749.11
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.44
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000086782

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.74
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999983498

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 2.96e-3
p-value of test                       :    0.9970

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.11
p-value of test                       :    0.98

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:40.22

 All tests were passed




Server wird beendet - Lösche Semaphor 115277848.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:53.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:05.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:55.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:00.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    2.26
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:44.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.30
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:11.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.88
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.32
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.77
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.12
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.79
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.08
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:43.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:02.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7230.14
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.17
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.03
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:05.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.51
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.25
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:32.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5010.49
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:59.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45846
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869846
  j =  1                              :        399908313
  j =  2                              :            45836
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45794
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869794
  j =  1                              :        399908412
  j =  2                              :            45794
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:27.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:01.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:33.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 8.41e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.96e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.086
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:34.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:34.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.49
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.86
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.33
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.56
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:38.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.84
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.32
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.13
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17609.38
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.54
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.65
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.77
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.60
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.13
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.14
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.40
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.46
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.51
p-value of test                       :  9.7e-3


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.77
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.37
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.15
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.29
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.43
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.75
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.50
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.97
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.84
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.20
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.62
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.78
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  453.05
p-value of test                       :  4.8e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.95
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.93
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.42
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.70
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.10
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.70
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:21.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.67
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:21.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 8.37e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.56
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.79
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.92
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:07.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:09.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9873.91
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10168.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    3.58
p-value of test                       :  1.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:41.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.86
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.80
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4226.32
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11710.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11750.40
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.72
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999940109

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.61
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999983024

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    2.57
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:54.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 92  HammingCorr, L = 30             1.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 116293656.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  1.9e-3


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1464
p-value of test                       :  3.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334584
  j =  1                              :        599997072
  j =  2                              :             1464
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5466
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:52.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:05.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:05.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:56.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7513
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:04:00.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.16
p-value of test                       :    0.9976


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:10.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.82
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    2.54
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    3.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:40.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.27
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.62
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.79
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.98
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.03
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.38
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.76
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:44.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1525.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7239.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.68
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.38
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:05.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.19
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5108.83
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45792
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869792
  j =  1                              :        399908417
  j =  2                              :            45790
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45902
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869902
  j =  1                              :        399908198
  j =  2                              :            45898
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:25.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:27.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:18.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:34.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.92
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:48.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.10
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.54
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.19
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.06
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.70
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.01
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16978.66
p-value of test                       :    0.9926



-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.12
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.83
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.38
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.42
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.50
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.67
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.44
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.63
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.56
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.31
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.09
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.42
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.91
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.60
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.89
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.09
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.23
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.08
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.34
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.54
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.29
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4885.01
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.79
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.17
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.46
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.99
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4867.88
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.24
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.82
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:34.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.33
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:22.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.82
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:21.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.12e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.68e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   23.20
p-value of test                       :  3.1e-3

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.97
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.51
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.02
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:08.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9878.32
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:38.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5080.22
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.61
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:49.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4023.72
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4208.79
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12088.12
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11691.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.40
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999984869

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.27
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999963878

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.69
p-value of test                       :    0.05

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :  -0.021
p-value of test                       :    0.51

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.5e-3

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    1.95
p-value of test                       :    0.03

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    2.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:52.07

 All tests were passed




Server wird beendet - Lösche Semaphor 117211160.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5484
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:53.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4479
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:04.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:55.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:59.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    5.20
p-value of test                       :  2.3e-3

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.86
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:12.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    2.03
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.81
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.13
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.74
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.76
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.00
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:59.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7021.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.14
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:05.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.65
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.30
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5055.14
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:07.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45833
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869833
  j =  1                              :        399908338
  j =  2                              :            45825
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46099
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870099
  j =  1                              :        399907808
  j =  2                              :            46087
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:26.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.54
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9934


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:18.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:02.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  7.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.97
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:34.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 9.81e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 5.74e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:39.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.40
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.67
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.32
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.81
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.75
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.96
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-3
p-value of test                       :    0.9979

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.48
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17225.64
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.85
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.04
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.84
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.46
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.10
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.24
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.53
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.52
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.64
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.33
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.03
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.66
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.89
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.27
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.95
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.55
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.75
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.73
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.51
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.97
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.79
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.03
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.35
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.64
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.64
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.23
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.18
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.14
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:23.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.43
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:20.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.02
p-value of test                       :    0.98

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 9.38e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.29e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.96
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.87
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:04.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.5e-3

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.89
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:05.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.42
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9836.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:43.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.89
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4771.12
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:50.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.06
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3905.46
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.36
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.65
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.43
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999900974

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.62
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999796118

Normal statistic for number of bits   :   -1.61
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    2.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:34.54

 All tests were passed




Server wird beendet - Lösche Semaphor 118161432.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:11.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5469
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:57.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:04.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:04.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:56.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:00.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.93
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    3.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.87
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:12.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.01
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.85
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.62
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.68
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.86
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.37
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.66
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.75
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.53
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7201.07
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.25
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.64
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:04.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.99
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.42
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:34.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5009.81
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:11.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45766
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869766
  j =  1                              :        399908473
  j =  2                              :            45756
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45880
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869880
  j =  1                              :        399908243
  j =  2                              :            45874
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:27.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  8.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:18.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:01.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:34.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.51e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 9.41e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:38.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:37.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.50
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.85
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.98
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.15
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.65
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.38
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.66
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.88
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.96e-3
p-value of test                       :    0.9948

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  100.46
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17655.80
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.15
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.21
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.78
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.99
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.13
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.65
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.15
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.09
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.07
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.03
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.94
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.95
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.12
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.31
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.76
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.42
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.40
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.97
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.88
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.44
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.66
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.06
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.93
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.59
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.85
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.52
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.20
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.66
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.97
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:22.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.45
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:21.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 5.67e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.94e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 8.45e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.68
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.22
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.43
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:04.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:04.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10118.77
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:43.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.95
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.67
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.95
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.88
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.41
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11793.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.61
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999988316

Normal statistic for number of bits   :  -0.092
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.54
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999867722

Normal statistic for number of bits   :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:09.09

 All tests were passed




Server wird beendet - Lösche Semaphor 119144472.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5316
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:55.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7126
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:04.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:04.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:54.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:59.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:12.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    2.76
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:42.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.45
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.26
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.33
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.68
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.93
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:45.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.20
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6902.66
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.54
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.66
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:07.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.36
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.26
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:33.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5187.85
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:11.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45990
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869990
  j =  1                              :        399908024
  j =  2                              :            45982
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45873
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869873
  j =  1                              :        399908254
  j =  2                              :            45873
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:26.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :  4.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 8.08e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:35.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.34
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.79
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.69
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:48.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.58
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:38.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.21
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.71
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.11
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17162.59
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.53
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.64
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.61
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.06
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.66
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.30
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.67
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.86
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.57
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.34
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.77
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.07
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  427.87
p-value of test                       :    0.9913


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.14
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.49
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.45
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.69
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.67
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.45
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.75
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.33
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.02
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.37
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.62
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:34.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.66
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.75
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.46
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.68
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.15
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:34.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.73
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:20.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.33
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -1.37
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:20.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.99
p-value of test                       :    0.98

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.71e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.00e-2
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.02e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.44
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.88
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.34
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:03.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.61
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.82
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9750.98
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:43.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.21
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.66
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:50.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3997.00
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4228.16
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11797.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.43
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.83
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000028711

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.44
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000001558

Normal statistic for number of bits   :   0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.32
p-value of test                       :    0.01

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.45e-3
p-value of test                       :    0.9964

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.4e-3

Anderson-Darling statistic = A2       :    5.42
p-value of test                       :  1.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.31
p-value of test                       :  4.7e-4    *****

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   0.028
p-value of test                       :    0.49

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:35.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 105  AutoCor, d=1, r=27              4.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 120127512.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:56.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4221
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:41.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:06.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:06.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:56.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:02.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.61
p-value of test                       :  4.5e-3

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     844
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:13.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    2.01
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:41.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.16
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.62
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.74
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1371.26
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7122.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:41.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.53
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:04.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.77
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.13
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4934.91
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:53.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45867
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869867
  j =  1                              :        399908271
  j =  2                              :            45857
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45899
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869899
  j =  1                              :        399908203
  j =  2                              :            45897
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:26.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-3
p-value of test                       :    0.9977

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  5.3e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:18.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:32.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 8.53e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 5.48e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.73
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:35.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:48.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.05
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.21
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:47.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.46
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.93
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:39.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.50
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    4.16
p-value of test                       :  7.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   20.02
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.02
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.039
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17252.31
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.62
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.91
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.21
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.06
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.34
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.59
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.65
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.02
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.80
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.53
p-value of test                       :  9.7e-3


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.43
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.31
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.24
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.18
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.88
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.46
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.15
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.76
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.12
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.91
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.17
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.96
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4878.24
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.64
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.48
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.79
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.32
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5246.49
p-value of test                       :  7.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.77
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.52
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.51
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.84
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:22.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.07e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.14e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.69
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.88
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.90
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:04.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:05.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10178.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10114.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.043
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:40.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.44
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:44.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5083.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12067.91
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11843.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.78
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999899615

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.43
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000258430

Normal statistic for number of bits   :    2.04
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.15

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:47.75

 All tests were passed




Server wird beendet - Lösche Semaphor 121143320.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997195
  j =  2                              :             1401
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1260
p-value of test                       :    0.9978

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334380
  j =  1                              :        599997480
  j =  2                              :             1260
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5495
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:41.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:36.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:34.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:54.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4242
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:55.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:01.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:01.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:53.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:58.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.16
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.07
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.95
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    4.24
p-value of test                       :  6.7e-3

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:10.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.86
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    2.30
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:35.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.14
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.63
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.12
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.11
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.24
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.58
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.41
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  391.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7092.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:01.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.40
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.71
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5017.83
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:13.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46053
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870053
  j =  1                              :        399907897
  j =  2                              :            46047
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45610
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869610
  j =  1                              :        399908784
  j =  2                              :            45602
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:27.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:17.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:52.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:33.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.82e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.19e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.097
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:38.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.97
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.37
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.35
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.07
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.01
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:31.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   17.08
p-value of test                       :  6.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.17
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17139.19
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.98
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.64
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.87
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.15
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.67
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.10
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.01
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.25
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.39
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.15
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.70
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.27
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.21
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.62
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.42
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:48.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.92
p-value of test                       :  8.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.01
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.73
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.16
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.05
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:46.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.97
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.63
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.84
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  444.26
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.30
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.22
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.67
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5090.78
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.15
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.19
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:33.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.95
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -1.95
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:12.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.23
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:13.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.28e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:47.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.71e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 4.59e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.76
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.86
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.21
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:10.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:10.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10190.20
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : -3.42e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:52.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4747.22
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.73
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:49.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.50
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3927.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12108.13
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11903.28
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.54
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999970802

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.27
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999968315

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:35.26
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 69  MatrixRank, L=1000, r=26        6.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 102400025.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5485
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:43.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:35.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:54.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:55.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:01.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:01.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:52.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:58.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.49
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    3.67
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:45.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.15
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:12.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:37.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.70
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.42
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.75
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  190.68
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  494.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.53
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:02.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6949.99
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.95
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.48
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:02.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   15.14
p-value of test                       :  9.8e-3


-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.12
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4985.99
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:59.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45679
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869679
  j =  1                              :        399908646
  j =  2                              :            45671
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45765
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869765
  j =  1                              :        399908473
  j =  2                              :            45759
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :  3.1e-3

Kolmogorov-Smirnov- statistic = D-    : 6.26e-4
p-value of test                       :    0.9994    *****

Anderson-Darling statistic = A2       :    4.38
p-value of test                       :  5.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9984


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:19.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:53.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:33.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 2.41e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 7.58e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:32.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:33.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.80
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.29
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.52
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.01
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.61
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.94
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:40.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.49
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.30
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.43
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17270.47
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.85
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.50
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.91
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.99
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.63
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.65
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.52
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.68
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.71
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.10
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.20
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.47
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.86
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.34
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.68
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:46.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.57
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.31
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.51
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.30
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.01
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.25
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.52
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4871.89
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.02
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.62
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.97
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.79
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.60
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.88
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.09
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.09
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -2.26
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:18.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.10
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -1.70
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:16.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.22e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 8.52e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.01e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.26
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.69
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.50
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:09.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.09
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:09.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.51
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9856.93
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:44.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4968.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
p-value of test                       :    0.9921

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4745.11
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.77
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11635.76
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11552.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.44
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000025030

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.32
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999941906

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.22
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:29.59

 All tests were passed




Server wird beendet - Lösche Semaphor 103284761.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5462
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:44.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:36.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:35.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:53.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:01.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:01.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:53.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:56.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.20
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:10.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:38.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.37
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.03
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.21
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.14
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  295.05
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.32
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1475.06
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:07.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7170.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.41
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:09.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.54
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.92
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5002.82
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:04.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45740
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869740
  j =  1                              :        399908523
  j =  2                              :            45734
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45710
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869710
  j =  1                              :        399908584
  j =  2                              :            45702
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:30.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:19.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:48.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:02.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:54.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 7.91e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:40.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:41.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.58
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.36
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.74
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.75
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.28
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.43
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17123.12
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.86
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.19
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.62
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.97
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.92
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.43
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.70
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.10
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.52
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.36
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  440.70
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.75
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.34
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.45
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.85
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.19
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.58
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.40
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.87
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.68
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.82
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.31
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:34.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.77
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4853.35
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.61
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.59
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:34.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.09
p-value of test                       :    0.9949


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:24.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.06
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:26.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    2.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.46e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.18e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.63
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.14
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.75
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:08.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.64
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:06.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9852.07
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.56
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -3.45
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:04:20.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:03.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4028.52
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:30.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.51
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11940.60
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:41.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11605.98
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:44.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.70
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999883643

Normal statistic for number of bits   :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.78
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999881408

Normal statistic for number of bits   :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    2.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:56.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 92  HammingCorr, L = 30             0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 103874585.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:50.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:38.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:54.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:02.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:02.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:54.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:00.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.51
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:13.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:42.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.16
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.34
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.29
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.09
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.68
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.73
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.23
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.88
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.77
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.66
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:06.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7101.30
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.80
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.72
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:08.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.76
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.01
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:37.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4960.93
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:56.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45902
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869902
  j =  1                              :        399908201
  j =  2                              :            45892
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45653
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869653
  j =  1                              :        399908695
  j =  2                              :            45651
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:29.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:18.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:05.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.84e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.10e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.75e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:38.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.037
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.58
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.49
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.15
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.13
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.32
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.83
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.98
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.43
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17222.21
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.48
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.85
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.91
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.83
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.03
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.62
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.48
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.76
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.36
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.57
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.61
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.05
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.39
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.94
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.61
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.51
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.85
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.90
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.00
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.56
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4900.87
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.72
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.00
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.60
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.04
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.70
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.28
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.32
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.56
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :    1.43
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:23.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.85
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:25.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.41e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.20e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 9.90e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.03
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.03
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.85
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:08.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:06.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9930.71
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9947.57
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.071
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.32
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:04:19.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.15
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:53.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.92
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4230.35
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3911.73
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11770.40
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11990.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:31.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.81
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000109753

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.49
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999993173

Normal statistic for number of bits   :  -0.054
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:19.39

 All tests were passed




Server wird beendet - Lösche Semaphor 105054233.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5503
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:49.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:38.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:37.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:02.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:02.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7119
p-value of test                       :    0.9902


-----------------------------------------------
CPU time used                    :  00:03:54.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:00.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    3.52
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:13.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:42.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.62
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.05
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  271.13
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.67
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:43.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.12
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:02.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7198.17
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.01
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.80
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:03.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.39
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.50
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:32.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4961.91
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:53.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45854
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869854
  j =  1                              :        399908294
  j =  2                              :            45850
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45998
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869998
  j =  1                              :        399908008
  j =  2                              :            45990
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9932


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:26.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:18.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:00.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:33.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.32e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 8.71e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:31.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:31.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.64
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.25
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.69
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.27
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.48
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.69
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.24
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.5e-3

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  171.47
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17152.52
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.46
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.82
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.39
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.03
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.74
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.58
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.59
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.47
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.87
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.38
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.69
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.42
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.19
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.83
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.12
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.66
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.50
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.73
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.64
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.73
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.84
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.34
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.76
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.01
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.48
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  323.47
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.67
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.13
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.64
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:34.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.57
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:24.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.11
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:24.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.40e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.15e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 3.97e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.87
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.82
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9920

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:06.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:09.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.23
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9921.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:43.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5024.64
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4733.82
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.07
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.77
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11825.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11825.15
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:29.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.82
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999971138

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.63
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999925430

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 6.38e-4
p-value of test                       :    0.9994    *****

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:13.51

 All tests were passed




Server wird beendet - Lösche Semaphor 106135577.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5318
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:50.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:39.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:38.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:02.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:03.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7566
p-value of test                       :  2.0e-3


-----------------------------------------------
CPU time used                    :  00:03:54.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:59.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:14.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:42.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.70
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.61
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.80
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  285.35
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.86
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:01.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7124.39
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:04.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.10
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.40
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4990.36
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:59.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45709
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869709
  j =  1                              :        399908588
  j =  2                              :            45697
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46044
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870044
  j =  1                              :        399907916
  j =  2                              :            46036
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:26.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:19.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:46.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:01.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:55.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.01e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.63
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:47.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:47.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.09
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:44.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.16
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.26
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17459.98
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.80
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.10
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.61
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.24
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.28
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.64
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.14
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.46
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.76
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.44
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.57
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.86
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.70
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.00
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.17
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.48
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.06
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.96
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.71
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.10
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.07
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.23
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.75
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.60
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5182.16
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  467.18
p-value of test                       :  1.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.25
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.72
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:21.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.24
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    0.29
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:22.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 6.41e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.38e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.76
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.11
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:06.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.29
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:08.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.48
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10169.46
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:49.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4727.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4661.82
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:01:50.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4015.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.47
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11663.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11737.24
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.91
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000168550

Normal statistic for number of bits   :    1.33
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.91
p-value of test                       :  8.5e-3


-----------------------------------------------
Total number of bits:  7999924962

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :  -0.085
p-value of test                       :    0.53

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:04.25

 All tests were passed




Server wird beendet - Lösche Semaphor 107151385.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5292
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:50.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:37.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4506
p-value of test                       :  5.4e-3


-----------------------------------------------
CPU time used                    :  00:01:54.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:02.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7142
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:02.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:53.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:59.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    6.25
p-value of test                       :  7.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:12.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.05
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:43.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.95
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.40
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.58
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.21
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.78
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.33
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.79
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.48
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:02.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7096.55
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.96
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:04.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.33
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   83.99
p-value of test                       :    0.9937


-----------------------------------------------
CPU time used                    :  00:01:35.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.04
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9955


-----------------------------------------------
CPU time used                    :  00:02:59.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45819
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869819
  j =  1                              :        399908364
  j =  2                              :            45815
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46003
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870003
  j =  1                              :        399907997
  j =  2                              :            45997
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:28.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:19.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.48e-3
p-value of test                       :    0.9914

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:34.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.58e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.36e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : 7.87e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.51
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.65
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.59
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.05
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:44.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.31
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.19
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.14
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17019.08
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.67
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.45
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.37
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   44.30
p-value of test                       :  7.0e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.78
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.75
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.97
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   51.19
p-value of test                       :  1.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.63
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.28
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.67
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.25
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.39
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.47
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.97
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.81
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.50
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  173.86
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.00
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.41
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.98
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.34
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.75
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  158.36
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.89
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.31
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4825.94
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.76
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.58
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.26
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:20.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.19
p-value of test                       :    0.9941


-----------------------------------------------
Normal statistic for number of jumps  :   0.070
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:23.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.80e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.58e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 7.50e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.39
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.67
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:07.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:08.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :  7.2e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    5.89
p-value of test                       :  1.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9562.47
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9819.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:46.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.45
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.40
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3980.13
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12056.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11719.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.32
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999995954

Normal statistic for number of bits   :  -0.032
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.81
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999890273

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   0.050
p-value of test                       :    0.48

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.30
p-value of test                       :    0.99

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:37.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP2S, t = 9         7.6e-4
 90  HammingWeight2, r = 0           0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 108199961.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:50.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4456
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:37.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:55.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:03.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:03.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:54.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:59.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    2.40
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     543
p-value of test                       :    0.9903

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:12.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.30
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.41
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.48
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.90
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.22
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  361.39
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.64
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7127.60
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:01.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.23
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.78
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:35.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4857.46
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:54.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45928
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869928
  j =  1                              :        399908146
  j =  2                              :            45924
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45559
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869559
  j =  1                              :        399908887
  j =  2                              :            45549
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9975

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:26.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:17.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:01.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:54.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.69e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.92e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 3.63e-4
p-value of test                       :  5.1e-3

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:35.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:34.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:47.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.07
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.90
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.20
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.61
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.64
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.73
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.51e-3
p-value of test                       :    0.9985

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.55
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.34
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17373.87
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.03
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.73
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.01
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.14
p-value of test                       :    0.9973


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.13
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.77
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.91
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.91
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.94
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.98
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.11
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.08
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.56
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.86
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.79
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.68
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.74
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.02
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.02
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.72
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.61
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.09
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.12
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.63
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.14
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  320.89
p-value of test                       :    0.9916


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.94
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.34
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.73
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.80
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:21.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.06
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:22.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 9.35e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.85e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.08
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.00
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:04.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.50
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10250.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:43.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4740.48
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.64
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.53
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.93
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12078.77
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11679.10
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.54
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999996335

Normal statistic for number of bits   :  -0.029
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.22
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000066220

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:04.94

 All tests were passed




Server wird beendet - Lösche Semaphor 109150233.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5356
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:53.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:39.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4203
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:02.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:04.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:54.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:58.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     641
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.68
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:10.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.04
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    2.03
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:36.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.29
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.79
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.73
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.60
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.23
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.52
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.18
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.30
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.55
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:45.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7130.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:41.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.86
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.31
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:02.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.67
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.86
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5104.47
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:53.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45982
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869982
  j =  1                              :        399908039
  j =  2                              :            45976
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45725
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869725
  j =  1                              :        399908552
  j =  2                              :            45721
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:26.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:17.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.85e-3
p-value of test                       :    0.9947

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:01.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 9.23e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.76e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:32.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.99
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.40
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.14
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.00
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.80
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.98
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:11.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.61
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.48
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.28
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.76
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17402.59
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.83
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.44
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.02
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.51
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.79
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.29
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.99
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.43
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.17
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.55
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.69
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.00
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.66
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.26
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.62
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.15
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.71
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.77
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.42
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.84
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.31
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.74
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.87
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.13
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.26
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.00
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.46
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4775.59
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.17
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.51
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    1.30
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:20.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.43
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :    1.39
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:21.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    3.47
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -1.92
p-value of test                       :    0.97

Sample variance                       :    0.16
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.03e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.36
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.27
p-value of test                       :  9.4e-3

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.60
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:04.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.17
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:04.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.09
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.01
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:43.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4759.49
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:51.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3813.03
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4224.68
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12023.40
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.54
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:29.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.83
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999890717

Normal statistic for number of bits   :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.18
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000007324

Normal statistic for number of bits   :   0.058
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.028
p-value of test                       :    0.49

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:09.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 97  HammingIndep, L=300, r=0        0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 110133273.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.91

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5474
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:54.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4178
p-value of test                       :    0.9922


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:04.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:55.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:58.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    2.86
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    3.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:11.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9945

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.56
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.68
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.54
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.42
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.38
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.61
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.52
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.93
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1370.98
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7050.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.44
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:00.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.29
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.75
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4975.59
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:56.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45602
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869602
  j =  1                              :        399908803
  j =  2                              :            45588
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45420
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869420
  j =  1                              :        399909163
  j =  2                              :            45414
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:26.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:18.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
p-value of test                       :    0.9914

Anderson-Darling statistic = A2       :    4.88
p-value of test                       :  3.4e-3


-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:54.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:33.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.10e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.77e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.36
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:32.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.96
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.60
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.52
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.89
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:38.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.72
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17247.15
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.30
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.04
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.40
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.65
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.32
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.10
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.00
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.44
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.65
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.65
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.65
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.37
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.43
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.00
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.98
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.87
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.76
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.27
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.79
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.80
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.39
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.27
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.78
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.74
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.56
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  318.88
p-value of test                       :    0.9933


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.81
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.58
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.82
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:34.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.87
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:22.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.70
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:22.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.90
p-value of test                       :    0.03

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 2.58e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.61
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.74
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.85
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:05.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:04.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10025.42
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:40.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.43
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.26
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.62
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11850.59
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11955.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.77
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999890051

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.78
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000000244

Normal statistic for number of bits   : 1.93e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   0.040
p-value of test                       :    0.48

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:12.63

 All tests were passed




Server wird beendet - Lösche Semaphor 111050777.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5413
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:55.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:57.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:05.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:54.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:59.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:51.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:13.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:41.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.73
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.75
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.00
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.76
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.74
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  280.77
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.58
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.42
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6960.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.92
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:05.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.51
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:30.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5039.93
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:53.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45454
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869454
  j =  1                              :        399909096
  j =  2                              :            45446
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45488
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869488
  j =  1                              :        399909031
  j =  2                              :            45474
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  4.2e-3

Anderson-Darling statistic = A2       :    5.21
p-value of test                       :  2.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  2.1e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:27.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:32.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.38e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 8.66e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.67e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.42
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.74
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.25
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.65
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.45
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:38.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.64
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.02
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17305.59
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:52.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.66
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.69
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.77
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.71
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.94
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.15
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.74
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.51
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.78
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.96
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.75
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.32
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.82
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.32
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.64
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.76
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.94
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.34
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.65
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.57
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.79
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.83
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4892.13
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.91
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.57
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.21
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.86
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.78
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.35
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.49
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -1.46
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:22.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.51
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:22.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.11e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.66e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 3.07e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.34
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.29
p-value of test                       :    0.9957

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.09
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:05.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.83
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:06.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.3e-3

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10332.84
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9869.20
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:38.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.59
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.12
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4337.52
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.42
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11946.42
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12124.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.09
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000048556

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.06
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000027220

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   0.014
p-value of test                       :    0.49

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:58.94

 All tests were passed




Server wird beendet - Lösche Semaphor 111935513.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:57.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7550
p-value of test                       :  3.6e-3


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:57.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:05.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:54.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:58.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:51.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    2.24
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     549
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:16.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.95
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.56
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.90
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.71
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.86
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.36
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.51
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.87
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:02.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6930.62
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.47
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.57
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:04.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.41
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   90.28
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:34.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4965.91
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:59.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46395
p-value of test                       :  8.2e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870395
  j =  1                              :        399907213
  j =  2                              :            46389
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46033
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870033
  j =  1                              :        399907940
  j =  2                              :            46021
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:28.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:19.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:01.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:32.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.60e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 8.25e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.020
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:37.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.84
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.94
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.76
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.16
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.44
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:41.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-3
p-value of test                       :    0.9989

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.87
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.18
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.33e-3
p-value of test                       :    0.9987

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   93.76
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17696.34
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.44
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.52
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.73
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.69
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.08
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.96
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.69
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.39
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.71
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.63
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.36
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.58
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.47
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.02
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.25
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.96
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.25
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.45
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.35
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.24
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.09
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  324.11
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.37
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.05
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.97
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.73
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.32
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.15
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.58
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.39
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.97
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -1.30
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:21.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.61
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:22.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 3.73e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.74e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.53
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.71
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9929

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.10
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:05.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9783.08
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.74
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.092
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:41.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.44
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.04
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12144.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11807.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.65
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999970436

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.07
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000027109

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:23.52

 All tests were passed




Server wird beendet - Lösche Semaphor 112853017.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1246
p-value of test                       :    0.9994    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334366
  j =  1                              :        599997508
  j =  2                              :             1246
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:57.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:42.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4233
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:06.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:05.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:57.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:02.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:50.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:14.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:43.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.10
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.63
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.47
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:11.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.73
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.22
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.32
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.23
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.16
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:03.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6995.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.38
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.57
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.34
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:35.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5092.73
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:53.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45958
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869958
  j =  1                              :        399908087
  j =  2                              :            45952
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45815
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869815
  j =  1                              :        399908375
  j =  2                              :            45805
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:28.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:20.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:03.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.37e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.021
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:36.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.18
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.94
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.20
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.84
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:38.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.64
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.17
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17477.78
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:52.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.25
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.93
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.37
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.51
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.66
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.21
p-value of test                       :    0.9966


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.92
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.99
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.41
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.93
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.87
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.84
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.12
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.07
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.21
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.47
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.16
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.16
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  170.60
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.16
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.35
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.63
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.56
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.38
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.19
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.14
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.48
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.32
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.25
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.29
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -1.65
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:20.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.62
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:20.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    0.17
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 6.54e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.45e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 7.92e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.32
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.54
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.61
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:05.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.59
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:06.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10125.58
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.34
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:40.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4791.27
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:47.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3986.73
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.70
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11963.36
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.77
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000084781

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.08
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000000946

Normal statistic for number of bits   : 7.48e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:18.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  8  CollisionOver, t = 7            0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 113901593.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5510
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:57.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:42.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:59.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:07.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:07.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:59.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7115
p-value of test                       :    0.9914


-----------------------------------------------
CPU time used                    :  00:03:57.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:51.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.95
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:12.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:42.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.37
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.93
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.07
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.26
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.40
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.50
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:01.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7074.64
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:01.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.11
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.71
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5159.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:51.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46233
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870233
  j =  1                              :        399907535
  j =  2                              :            46231
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45813
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869813
  j =  1                              :        399908375
  j =  2                              :            45811
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:28.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:18.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:59.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:35.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.33e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 3.28e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:37.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.65
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.14
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.72
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.96
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.62
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:45.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.47
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.23
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.24
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17346.11
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:52.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.72
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.99
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.58
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.51
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.57
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.27
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.79
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.89
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.09
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.32
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.95
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.36
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.99
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.41
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.97
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.23
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.18
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.30
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.61
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.12
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.81
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5143.09
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.27
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.46
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.77
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.58
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5104.85
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.74
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.65
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:34.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.71
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:20.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.21
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:21.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 9.87e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.49e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.40
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.73
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.95
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:04.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.29
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:05.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.29
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10099.08
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:51.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4979.43
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.80
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:50.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4254.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.96
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.16
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11694.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.90
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000038884

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.59
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999913523

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.093
p-value of test                       :    0.46

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.17
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:06.38

 All tests were passed




Server wird beendet - Lösche Semaphor 114819097.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1481
p-value of test                       :  9.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334601
  j =  1                              :        599997038
  j =  2                              :             1481
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5472
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:58.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:45.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4453
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:01.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:02.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7163
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:12.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:08.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:13.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    2.16
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.92
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:13.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.16
p-value of test                       :    0.9975

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:41.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.63
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.84
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.96
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.75
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.33
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  262.52
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:30.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.88
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:56.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.67
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:08.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7001.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:58.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.19
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:22.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.44
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.23
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:10.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5129.64
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:30.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:21.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45662
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869662
  j =  1                              :        399908683
  j =  2                              :            45648
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46004
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870004
  j =  1                              :        399907996
  j =  2                              :            45996
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:33.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:12.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:57.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.99e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 3.94e-4
p-value of test                       :  2.0e-3

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.032
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:44.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.34
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.33
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.63
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:54.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.37
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.46
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.26
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17386.98
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.13
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.71
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.38
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.58
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.22
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.82
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.43
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.24
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.10
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.75
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.31
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.46
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.41
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.94
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.22
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.37
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  567.08
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.72
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.99
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.97
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.00
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.10
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.39
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.06
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  308.96
p-value of test                       :    0.9980


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4845.09
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.05
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.87
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.62
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    1.18
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:22.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.96
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 8.39e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.72e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.71
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.47
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.82
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:04.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  245.90
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:05.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10117.13
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10242.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:04:39.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4775.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:53.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:57.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3953.65
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.02
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11778.46
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:35.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.88
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000017410

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.89
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999950990

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.4e-3

Kolmogorov-Smirnov- statistic = D-    : 1.49e-3
p-value of test                       :    0.9985

Anderson-Darling statistic = A2       :    4.43
p-value of test                       :  5.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -3.01
p-value of test                       :    0.9987

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.9998    *****

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:48.85
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           9.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 115900441.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5339
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:58.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:41.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:57.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:05.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:05.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:57.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:01.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:12.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.97
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:39.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.60
p-value of test                       :    0.9990    *****

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.21
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.13
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.83
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.63
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:05.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6950.16
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.35
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :  3.9e-4    *****

Anderson-Darling statistic = A2       :    4.17
p-value of test                       :  7.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:09.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.42
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.50
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5017.39
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:54.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45559
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869559
  j =  1                              :        399908884
  j =  2                              :            45555
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46025
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870025
  j =  1                              :        399907955
  j =  2                              :            46015
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:29.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.89e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.41
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.77
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.29
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.61
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.86
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.51
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.11
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.10
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.65
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.45
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:40.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17254.28
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.24
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.80
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.38
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.22
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.48
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.58
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.37
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.15
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.65
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.39
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.64
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.11
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.94
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.04
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.21
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.32
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.16
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.43
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.88
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.13
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.79
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4872.51
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.71
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.41
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.50
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.61
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.56
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.18
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.15
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.60
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   0.025
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:22.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.53
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:22.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.76e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 6.61e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.70
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.54
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.00
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:04.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.54
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.78
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.76
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.099
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:04:18.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:53.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3959.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3994.88
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.05
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:31.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.44
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:31.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.42
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000184942

Normal statistic for number of bits   :    1.46
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.85
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999984029

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:50.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 27  SimpPoker, r = 27               0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 117047321.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:55.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4153
p-value of test                       :    0.9975


-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4194
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:03.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:59.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.33
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:14.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.91
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.89
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:42.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.35
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.58
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.52
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.44
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  267.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.18
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.93
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:02.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7009.50
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.70
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:03.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.75
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.79
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:34.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5041.84
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:56.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45738
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869738
  j =  1                              :        399908527
  j =  2                              :            45732
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46087
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870087
  j =  1                              :        399907827
  j =  2                              :            46085
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:26.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:20.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:02.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:55.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:36.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 7.04e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 4.64e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.99
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:48.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.12
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.63
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:37.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.71
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.51
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.23
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17301.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.14
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.39
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.09
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.53
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.71
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.24
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.90
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.56
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.18
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.55
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.06
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.00
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.98
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.74
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.45
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.35
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.59
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.62
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.76
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.75
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.63
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.94
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.02
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.16
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.33
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.16
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.96
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.15
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:24.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.21
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :    1.66
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:23.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.70
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.81
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.15
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:04.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.83
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:05.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.03
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9902.05
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.039
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:44.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5047.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3987.84
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4259.89
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11713.91
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11650.05
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.97
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000027139

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.10
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999957569

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:57.05

 All tests were passed




Server wird beendet - Lösche Semaphor 118128665.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:47.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:58.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:04.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7165
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:04.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:55.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:00.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:45.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.13
p-value of test                       :  2.6e-3

Test on the Nm values of W_{n,i}(mNP1):    2.58
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     647
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:13.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:38.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.20
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.83
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.90
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.78
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.17
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7026.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.42
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.02e-3
p-value of test                       :    0.9969

Kolmogorov-Smirnov- statistic = D-    :    0.62
p-value of test                       :  1.4e-4    *****

Anderson-Darling statistic = A2       :    8.16
p-value of test                       :  1.1e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :  109.13
p-value of test                       :  1.1e-4    *****

-----------------------------------------------
CPU time used                    :  00:03:05.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.97
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.31
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:29.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5003.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:01.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46298
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870298
  j =  1                              :        399907407
  j =  2                              :            46292
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45896
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869896
  j =  1                              :        399908211
  j =  2                              :            45890
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:27.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:19.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:46.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.21e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.03e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:39.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:38.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.90
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.26
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:48.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.42
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.26
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.05
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.25
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.61
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:39.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17197.55
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.56
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.74
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.83
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.96
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.56
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.86
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   71.55
p-value of test                       :  2.6e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   45.40
p-value of test                       :  7.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.14
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.46
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.36
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.54
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.18
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.53
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.29
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.25
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.06
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.74
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.73
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.88
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.39
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  301.03
p-value of test                       :    0.9986


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.41
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:34.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.20
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.57
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4838.05
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.02
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.06
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:34.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.99
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -1.57
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:22.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.32
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -1.00
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:22.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    4.27
p-value of test                       :  6.8e-3

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    3.99
p-value of test                       :  4.2e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.49e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 7.32e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.56
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.34
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.25
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:05.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.84
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:05.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9865.60
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:43.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.17
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:47.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:50.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.77
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12017.49
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.38
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.79
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000021541

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.41
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000104104

Normal statistic for number of bits   :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :  -0.061
p-value of test                       :    0.52

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:03.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 39  Run, r = 15                     1.1e-4
 75  RandomWalk1 M (L=50, r=25)      2.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 119111705.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5517
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:59.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:54.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:02.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:12.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:31.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:29.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:11.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:43.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.68
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:13.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:39.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.10
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.16
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.55
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.89
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.59
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.47
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.92
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.77
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.32
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.24
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:36.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.48
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7090.42
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:43.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.85
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:07.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.56
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.30
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4893.87
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:59.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45924
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869924
  j =  1                              :        399908157
  j =  2                              :            45914
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869769
  j =  1                              :        399908466
  j =  2                              :            45761
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:27.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.90e-3
p-value of test                       :    0.9944

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  8.7e-3

Anderson-Darling statistic = A2       :    4.28
p-value of test                       :  6.5e-3


-----------------------------------------------
CPU time used                    :  00:02:24.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:11.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:54.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:33.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.83e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.60e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:37.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:37.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.39
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.71
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.30
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.25
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.13
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.72
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:03.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.53
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.06
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17450.23
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.03
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.92
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.85
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.73
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.72
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.26
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.30
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.23
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.40
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.94
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.73
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.22
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.24
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.04
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.31
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.94
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.37
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  427.43
p-value of test                       :    0.9917


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.73
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.67
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.61
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.10
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.81
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.38
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.36
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:50.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  312.57
p-value of test                       :    0.9969


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.44
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.78
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.77
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.67
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.88
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:21.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.55
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :    1.84
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:21.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.96e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 8.95e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.68
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.64
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.90
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:04.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:04.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10234.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9862.12
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.041
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:43.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.71
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.54
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:49.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.09
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4264.13
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.39
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11765.87
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.12
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000017980

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:13.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.50
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000136186

Normal statistic for number of bits   :    1.08
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:14.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.15

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:00.79

 All tests were passed




Server wird beendet - Lösche Semaphor 120094745.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5356
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:56.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:44.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:12.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7122
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:05.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:07.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:15.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.33
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.97
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.96
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.90
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.08
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.06
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:09.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6956.35
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:55.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.91
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.81
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.49
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.95
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:38.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5021.39
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:16.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45613
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869613
  j =  1                              :        399908776
  j =  2                              :            45609
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45649
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869649
  j =  1                              :        399908709
  j =  2                              :            45635
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:31.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:19.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:06.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 3.21e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.46
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.74
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.77
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.96
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.02
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.63
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17565.00
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.89
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.24
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.81
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.67
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.64
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.26
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.19
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.25
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.60
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.98
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.71
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.88
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.96
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.26
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.73
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.47
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.92
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.49
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.87
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.94
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.43
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.16
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.26
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.88
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.28
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.70
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.50
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.09
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.12
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.82
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.88
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:22.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         : -5.43e-3
p-value of test                       :    0.50

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.50e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.39
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.13
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.74e-3
p-value of test                       :    0.9982

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.73
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9919

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.16
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:07.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.94
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:04:11.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.08
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:49.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.28
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:52.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.86
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11572.05
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11779.47
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.45
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000058804

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.68
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000138373

Normal statistic for number of bits   :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:33.92

 All tests were passed




Server wird beendet - Lösche Semaphor 121110553.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1464
p-value of test                       :  3.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334584
  j =  1                              :        599997072
  j =  2                              :             1464
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5482
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:41.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:35.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:34.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:53.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:54.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:00.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:00.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:53.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:58.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:14.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    2.05
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:38.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.49
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.16
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.88
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.51
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  484.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.73
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7073.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:46.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.27
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:02.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.92
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.93
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:36.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5046.97
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:12.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46089
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870089
  j =  1                              :        399907824
  j =  2                              :            46085
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46027
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870027
  j =  1                              :        399907950
  j =  2                              :            46019
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:27.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:17.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:44.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:51.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:33.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 7.92e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:35.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:36.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.74
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.86
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.55
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.69
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.11
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.33
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.99
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.21
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:32.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.34
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17627.79
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.86
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.83
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.84
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.30
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.26
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.16
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.74
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.94
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.38
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.05
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.83
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.13
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.22
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.92
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.21
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.04
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.22
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.78
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:47.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.08
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.94
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.88
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.58
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.89
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.78
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.52
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.13
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.43
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.68
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:14.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.84
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:12.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:11.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.27e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.90
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.13
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.31
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:09.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.95e-3
p-value of test                       :    0.9926

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.0e-3

Anderson-Darling statistic = A2       :    5.97
p-value of test                       :  1.1e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  270.99
p-value of test                       :  6.1e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:10.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10099.98
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.40
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.025
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:44.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.73
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.75
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:49.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4287.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11434.50
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.14
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.40
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999927158

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.91
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999980999

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.29
p-value of test                       :    0.01

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:34.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 89  PeriodsInStrings, r = 20        6.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 102432794.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1252
p-value of test                       :    0.9989

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334372
  j =  1                              :        599997496
  j =  2                              :             1252
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:44.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:36.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:05.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:06.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:03.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:07.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    4.30
p-value of test                       :  6.2e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     817
p-value of test                       :    0.9973

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:10.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.03
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.31
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    3.10
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     177
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.96
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.97
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.63
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.61
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:29.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.97
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1519.05
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:06.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7036.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.48
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.31
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:18.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.66
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.83
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5151.20
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:18.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45979
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869979
  j =  1                              :        399908044
  j =  2                              :            45975
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45951
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869951
  j =  1                              :        399908102
  j =  2                              :            45943
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:33.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:19.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:04.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.02e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.70e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.66e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:24.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.86
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.48
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.06
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.12
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.97
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.86
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.04
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.40
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17358.10
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.10
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.12
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.49
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.26
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.40
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.80
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.69
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.55
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.25
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.26
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.16
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.03
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.48
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.59
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.15
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.35
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.89
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.49
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.95
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.94
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.39
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.57
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  469.56
p-value of test                       :  9.1e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.43
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.83
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.24
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5088.47
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.51
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.13
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.15
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:26.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.67
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:24.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.01e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.73
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.05
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.38
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:06.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9952

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:07.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10004.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9841.67
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:04:31.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.71
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4765.43
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:58.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4249.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.25
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11844.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:35.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.88
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:39.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.17
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999754616

Normal statistic for number of bits   :   -1.94
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.35
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999836750

Normal statistic for number of bits   :   -1.29
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:14:09.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 R (L=10000, r=0)    9.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 102989828.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5405
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:48.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:38.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7149
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:37.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:02.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:01.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:54.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:01.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:15.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:43.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.61
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.01
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  264.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  503.65
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1400.95
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:00.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6998.72
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.85
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:03.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.14
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.08
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:35.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5030.39
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:08.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45776
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869776
  j =  1                              :        399908453
  j =  2                              :            45766
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869892
  j =  1                              :        399908220
  j =  2                              :            45884
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:23.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:15.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  1.6e-3

Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
p-value of test                       :    0.9998    *****

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:54.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:33.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.19e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.30e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:32.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   98.01
p-value of test                       :  8.1e-3

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.19
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.41
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.47
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.73e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.30
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.66
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.87
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17464.98
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.03
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.08
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.10
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.79
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.64
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.76
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.06
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.53
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.40
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.13
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.63
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.98
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.52
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.40
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.05
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.58
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.61
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.18
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.52
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.64
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.94
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.98
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.67
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.27
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5131.01
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.48
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.14
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.53
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:25.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.00
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:24.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.95
p-value of test                       :    0.97

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 7.72e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.02
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.38
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:07.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9823.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10129.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:42.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.21
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.77
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.62
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.81
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11537.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11487.81
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.66
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999954722

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.91
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999893819

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:59.46

 All tests were passed




Server wird beendet - Lösche Semaphor 104431620.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5525
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:49.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:39.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:37.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:02.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:02.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:54.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7522
p-value of test                       :  9.0e-3


-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:13.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:43.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.31
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.68
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.92
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.56
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.39
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.73
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.54
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.47
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.11
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1524.36
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:59.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7006.50
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.30
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:02.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.98
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.55
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5139.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:59.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46131
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870131
  j =  1                              :        399907742
  j =  2                              :            46123
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45614
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869614
  j =  1                              :        399908774
  j =  2                              :            45610
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.70
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9972


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:29.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:19.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:01.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:54.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:32.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.01
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.39
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:48.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.22
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:40.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9900

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.39e-3
p-value of test                       :    0.9921

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.54
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17303.35
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.02
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.63
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.07
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.98
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.13
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.67
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.36
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.26
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.11
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.89
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.75
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.16
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.64
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.38
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.47
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.85
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.90
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.07
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.36
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.92
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5169.66
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.07
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.16
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.67
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.93
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5125.29
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.64
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.62
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.98
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    1.87
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:25.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.09
p-value of test                       :    0.9949


-----------------------------------------------
Normal statistic for number of jumps  : -1.49e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.96
p-value of test                       :  9.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.51
p-value of test                       :    0.9940

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.77e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.82e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.18
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.08
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.09
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:05.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9952.15
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.3e-3

Kolmogorov-Smirnov- statistic = D-    : 3.33e-3
p-value of test                       :    0.9966

Anderson-Darling statistic = A2       :    3.90
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9610.62
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:40.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.50
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4763.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.93
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.36
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11720.34
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.41
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.00
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999967895

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.10
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999971603

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.01
p-value of test                       :    0.02

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:23.65

 All tests were passed




Server wird beendet - Lösche Semaphor 105250820.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5480
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:51.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:37.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:02.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:02.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:01.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     547
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    2.26
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:13.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:41.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.80
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.64
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.87
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.82
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.38
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.37
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.82
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.51
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6992.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.44
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.31
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:03.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.06
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.90
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:33.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5147.58
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:53.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46206
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870206
  j =  1                              :        399907593
  j =  2                              :            46196
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46298
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870298
  j =  1                              :        399907409
  j =  2                              :            46288
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  8.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:27.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:18.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:46.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  9.0e-3

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:33.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : -6.27e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:48.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:47.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.83
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.71
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.79
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:40.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.12
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.72
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17316.33
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.67
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.05
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.60
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.69
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.64
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.81
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.19
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.57
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.81
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.23
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.34
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.10
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.65
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   98.66
p-value of test                       :    0.9933


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.24
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.03
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.60
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.71
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.14
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.76
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.53
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.44
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.26
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.14
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.36
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.38
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.72
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.15
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.51
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.79
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:25.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.95
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:23.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.44
p-value of test                       :  5.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.92
p-value of test                       :  1.7e-3

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    1.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.15e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.82
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.38
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.17
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:05.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:07.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9922.41
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10083.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:44.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5009.30
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.67
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.88
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4236.21
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11806.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11680.52
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.25
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999906551

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.50
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000123628

Normal statistic for number of bits   :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:30.11

 All tests were passed




Server wird beendet - Lösche Semaphor 106102788.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5497
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:02.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:53.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:14.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:14.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:34.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:34.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:05:01.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:05:00.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:13.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.87
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:42.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.85
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.10
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.90
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.95
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.73
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.05
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.30
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:59.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6906.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.12
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:02.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.66
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.09
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5038.43
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:55.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46255
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870255
  j =  1                              :        399907492
  j =  2                              :            46251
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46050
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870050
  j =  1                              :        399907903
  j =  2                              :            46044
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:27.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:18.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:01.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:33.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:31.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.25
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   98.83
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.98
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.99
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.29
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:38.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.64
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.98
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:29.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.66
p-value of test                       :  4.1e-5    *****

Anderson-Darling statistic = A2       :    6.48
p-value of test                       :  6.3e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  182.93
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17591.35
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.14
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.84
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.58
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.75
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.35
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.40
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.56
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.67
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.68
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.96
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  103.46
p-value of test                       :    0.9970


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.92
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.62
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.84
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.03
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.24
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.86
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.81
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.85
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.23
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.89
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.46
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.03
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.53
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.35
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.43
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.57
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.28
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.51
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.65
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.69
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:24.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.47
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :   -2.20
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:20.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.52
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.27
p-value of test                       :    0.99

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.02e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.17
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.54
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.68
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:07.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.91
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:07.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.22
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9924.17
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.081
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:45.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5011.32
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.47
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12064.73
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11566.86
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.19
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000131050

Normal statistic for number of bits   :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.67
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999988097

Normal statistic for number of bits   :  -0.094
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:17.64

 All tests were passed




Server wird beendet - Lösche Semaphor 107118596.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:52.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:38.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:55.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:01.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:02.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:54.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:58.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9918

Stat. AD after spacings (mNP2-S)      :    2.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9914

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:12.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.38
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.48
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.91
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   93.49
p-value of test                       :  6.9e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.41
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.96
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.31
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.85
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1509.78
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6786.17
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:43.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.94
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:03.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.44
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.91
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:35.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5129.70
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:54.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45880
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869880
  j =  1                              :        399908242
  j =  2                              :            45876
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45876
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869876
  j =  1                              :        399908253
  j =  2                              :            45866
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:27.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:19.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:03.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.34e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.60e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:33.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.05
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:47.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.69
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.64
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.85
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.3e-3

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.29
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.20
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.12
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17231.18
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.73
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.73
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   44.58
p-value of test                       :  9.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.16
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.06
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.02
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.01
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.55
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.48
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.81
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.30
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.72
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.00
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.70
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.11
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.38
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.88
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.66
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.66
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.28
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.89
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.16
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4842.14
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.74
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.66
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.77
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.84
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4834.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.25
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.77
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.36
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:23.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.39
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :   -1.20
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:23.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 7.26e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.00
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.67
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.78
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:06.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.71
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.053
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:46.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.94
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:48.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4996.81
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.54
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4359.31
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12083.93
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11673.30
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.94
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000033250

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.50
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000086059

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    2.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:40.57
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 30  CouponCollector, r = 0          6.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 108068868.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:55.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:38.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:02.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:01.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.93
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.14
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:12.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    2.05
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     175
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:35.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.25
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.15
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.04
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.61
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.08
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1398.27
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:06.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7234.07
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.68
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:15.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.18
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.81
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:37.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5048.78
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:54.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46442
p-value of test                       :  4.4e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870442
  j =  1                              :        399907122
  j =  2                              :            46430
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45801
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869801
  j =  1                              :        399908405
  j =  2                              :            45787
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:31.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:19.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 9.03e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:04.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:02.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.89e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 9.56e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 4.15e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:41.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.39
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.75
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.78
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.13
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.01
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.04
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.78
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:40.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17545.49
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.96
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.65
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.44
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.82
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.03
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.38
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.75
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.22
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.80
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.76
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.77
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.95
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.63
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.56
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.21
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.60
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.78
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.76
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.83
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.69
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.99
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.47
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.18
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.09
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.28
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.24
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.86
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.79
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:25.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.81
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:24.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.78e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 6.81e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.53e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.91
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.52
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.73
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:07.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:08.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9788.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10300.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:04:25.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.80
p-value of test                       :  3.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4596.28
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:01:57.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4706.18
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:58.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3983.33
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4293.40
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11873.77
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12158.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.68
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999931433

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.41
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000150655

Normal statistic for number of bits   :    1.19
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.87
p-value of test                       :    0.97

Sample variance                       :    2.63
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:43.77

 All tests were passed




Server wird beendet - Lösche Semaphor 109019140.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1469
p-value of test                       :  2.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334589
  j =  1                              :        599997062
  j =  2                              :             1469
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5233
p-value of test                       :    0.9948


-----------------------------------------------
CPU time used                    :  00:03:50.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:39.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:03.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7177
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:02.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:55.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:00.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.44
p-value of test                       :  5.4e-3

Test on the Nm values of W_{n,i}(mNP1):    2.21
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     960
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    3.87
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.01
p-value of test                       :  9.0e-3

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    3.62
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:11.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:34.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.63
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.22
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.78
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.63
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.56
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  190.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.07
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.44
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6929.59
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:40.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.39
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.21
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:01.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.67
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.85
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:35.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5130.90
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:52.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45799
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869799
  j =  1                              :        399908405
  j =  2                              :            45793
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45845
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869845
  j =  1                              :        399908312
  j =  2                              :            45841
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:26.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:19.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:01.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.21e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:31.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.34
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.10
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.19
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.48
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.86
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.13
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:37.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.25
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.74
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.10
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17819.62
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.15
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.54
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.92
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.18
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.51
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.89
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.44
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.52
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.72
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :   95.21
p-value of test                       :    0.9996    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.72
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.72
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.87
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.42
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.56
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.25
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.56
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.35
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.16
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.45
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.66
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.39
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.55
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.73
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.06
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.89
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.37
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.14
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.52
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.48
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :  -0.082
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:23.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.90
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:23.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         : 5.43e-3
p-value of test                       :    0.50

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.06e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 7.27e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.55e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.84
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.01
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.03
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:04.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:06.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.4e-3

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10319.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9891.57
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:43.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.63
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.61
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.26
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.85
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11803.37
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:29.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.07
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000183154

Normal statistic for number of bits   :    1.45
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.08
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000096916

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:52.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 H (L=1000, r=0)     0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 110231556.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5524
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:53.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:57.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:03.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:54.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:00.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    2.57
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     269
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    2.04
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:14.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:43.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.60
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.71
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.14
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.50
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  284.75
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.27
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.31
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7003.58
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:40.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.35
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:03.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.63
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.97
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:31.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5022.33
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:57.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45335
p-value of test                       :    0.9945


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869335
  j =  1                              :        399909332
  j =  2                              :            45331
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45369
p-value of test                       :    0.9914


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869369
  j =  1                              :        399909266
  j =  2                              :            45361
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:26.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:17.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :  1.6e-3

Kolmogorov-Smirnov- statistic = D-    : 8.71e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    6.83
p-value of test                       :  4.2e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9998    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:34.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.26e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.75
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.16
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.95
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.00
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.08
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.14
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:38.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.20
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.57
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.68
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.86
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.74
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17245.79
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.53
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.46
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.03
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.10
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.73
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.32
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.02
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.46
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.14
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.70
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.08
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.41
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  183.32
p-value of test                       :  4.3e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.17
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.32
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.61
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.84
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.72
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.17
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.17
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.00
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.81
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.82
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.00
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.67
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.15
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.95
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.99
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.99
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.66
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:22.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.14
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:22.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.75e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.04e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 6.20e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.15
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.59
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.85
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:07.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.30
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:06.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9904.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9805.91
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:40.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.06
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.38
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.40
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.63
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11645.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.03
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.43
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999958781

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.24
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000052810

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :  -0.022
p-value of test                       :    0.51

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :  -0.036
p-value of test                       :    0.51

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:08.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 48  MaxOft, t = 24                  0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 111149060.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:39.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5451
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:54.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:40.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:04.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:04.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:54.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:00.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9944


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    2.37
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:12.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.86
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:43.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.31
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.66
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.26
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.26
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.39
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.45
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.36
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.77
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.50
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1377.56
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7090.87
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.11
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.48
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:04.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   15.55
p-value of test                       :  8.3e-3


-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.07
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:35.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4940.67
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:52.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45439
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869439
  j =  1                              :        399909127
  j =  2                              :            45429
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46010
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870010
  j =  1                              :        399907981
  j =  2                              :            46008
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  3.8e-3

Anderson-Darling statistic = A2       :    4.09
p-value of test                       :  7.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:28.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:17.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:02.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.52e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:35.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.75
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.11
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.30
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.17
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:48.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.15
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.90
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.25
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.31
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17270.70
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.89
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.50
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.70
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.87
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.99
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.91
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.65
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.22
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.01
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.97
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.91
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  560.69
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.88
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.77
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.16
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.93
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.10
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.84
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.89
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.70
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.54
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.58
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.15
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.91
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.90
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4899.37
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.87
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.47
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.80
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:23.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.99
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :   0.030
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:24.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 9.04e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.34
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.04
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.75
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:06.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.34
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9701.52
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9933.33
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.037
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:45.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.25
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4814.40
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:51.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3974.25
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12003.00
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11910.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.22
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000002632

Normal statistic for number of bits   :   0.021
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.08
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999963206

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   0.042
p-value of test                       :    0.48

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:15.59

 All tests were passed




Server wird beendet - Lösche Semaphor 112099332.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1249
p-value of test                       :    0.9992    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334369
  j =  1                              :        599997502
  j =  2                              :             1249
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5370
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:57.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:43.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:42.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:59.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:08.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:08.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:02.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     944
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:46.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    3.40
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     547
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:12.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:40.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.66
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.77
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.85
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.33
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.79
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.35
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.56
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.59
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:51.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.13
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:05.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7124.33
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.87
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.95
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:14.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.47
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.01
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5118.30
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:58.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46020
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870020
  j =  1                              :        399907964
  j =  2                              :            46012
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45798
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869798
  j =  1                              :        399908407
  j =  2                              :            45792
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:30.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:19.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:47.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:37.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 9.03e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:43.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:44.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.70
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.84
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.07
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.92
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:51.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.82
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.67
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17123.62
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:51.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.92
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.18
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.96
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.81
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.24
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.74
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.78
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.18
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.17
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.57
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.34
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.92
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  106.91
p-value of test                       :  7.4e-3


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.27
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.16
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.93
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.39
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.56
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.98
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.11
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.77
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.71
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.22
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.13
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.71
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.39
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :  -0.064
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.37
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   0.034
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.55e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.99e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 7.74e-4
p-value of test                       :    0.9946

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.09
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.48
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.09
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.05
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9950.83
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.59
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:04:23.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.28
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:55.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4787.46
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:58.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4197.73
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.66
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11603.07
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:36.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11768.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:35.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.80
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000077554

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.91
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999954896

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :  -0.030
p-value of test                       :    0.51

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.23
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:29.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 113049604.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5526
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:54.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:03.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:55.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:59.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.13
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:13.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:39.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.27
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.75
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.27
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.58
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.71
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.75
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:45.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.35
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:59.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7190.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.34
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.60
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:01.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.61
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.42
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:36.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5065.25
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:57.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46113
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870113
  j =  1                              :        399907777
  j =  2                              :            46107
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46181
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870181
  j =  1                              :        399907643
  j =  2                              :            46171
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:27.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:17.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:33.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.38e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 2.14e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 4.71e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:34.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.34
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:00:48.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.21
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.57
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.49
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.99
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.81
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:40.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.75
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.50
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.57
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17607.92
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.61
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.39
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.99
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.97
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.56
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.39
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.57
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.59
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.35
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.39
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.37
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.43
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.19
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.27
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.60
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.85
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.01
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.60
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.19
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.17
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.36
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.20
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.87
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.05
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.48
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.21
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.57
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.19
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.38
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.22
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:21.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.15
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:22.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.23e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.01
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.21
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.06e-3
p-value of test                       :    0.9969

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.50
p-value of test                       :  5.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  267.53
p-value of test                       :  1.0e-3

-----------------------------------------------
CPU time used                    :  00:02:08.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9669.24
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.55
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:42.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4691.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.80
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12025.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11622.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.96
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999896675

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.40
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999965006

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.1e-3

Anderson-Darling statistic = A2       :    4.33
p-value of test                       :  6.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.70
p-value of test                       :  3.5e-3

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:42.54

 All tests were passed




Server wird beendet - Lösche Semaphor 114196484.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5490
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:55.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:38.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:57.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7482
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:03.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:04.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:54.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:00.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    2.27
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     827
p-value of test                       :    0.9927

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    8.10
p-value of test                       :  1.1e-4    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:12.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.90
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.33
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:43.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.06
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.80
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.73
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.05
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6829.75
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:25.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.31
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.63
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5123.53
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:52.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46048
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870048
  j =  1                              :        399907909
  j =  2                              :            46038
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45510
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869510
  j =  1                              :        399908982
  j =  2                              :            45506
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:27.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:18.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:59.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.21e-3
p-value of test                       :    0.9964

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.53e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:26.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.029
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.37
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.33
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.10
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:47.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.04
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.29
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17322.31
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.84
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.94
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.56
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.45
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.12
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.39
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.30
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.75
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.36
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.37
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.87
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.23
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.89
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.73
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.77
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.29
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.43
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.52
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.62
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.95
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.25
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.46
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.80
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.51
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.45
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.28
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.27
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.90
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.64
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.96
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -0.63
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:22.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.05
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :  -0.046
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.27e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.54e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.29
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.31
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:07.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.78
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:05.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.00
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9729.57
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.34
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.20
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.23
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.86
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11772.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11885.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.34
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000006739

Normal statistic for number of bits   :   0.053
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.82
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000012274

Normal statistic for number of bits   :   0.097
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.80
p-value of test                       :    0.96

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         : -1.80e-4
p-value of test                       :    0.50

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:07.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs NP, t = 9            1.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 115113988.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:58.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:43.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:59.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:09.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:09.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:06.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7137
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:11.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.13
p-value of test                       :  2.6e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    2.37
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     642
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:14.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    2.21
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:41.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.18
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.42
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.86
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.15
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.19
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.02
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.59
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.53
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.51
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1323.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:10.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7022.57
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.88
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:10.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.55
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.01
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4963.36
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:32.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:57.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45719
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869719
  j =  1                              :        399908563
  j =  2                              :            45717
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46167
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870167
  j =  1                              :        399907672
  j =  2                              :            46155
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:31.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:22.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:54.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:57.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:41.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.38e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.84
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.54
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.14
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.33
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:54.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.24
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17372.40
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.82
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.81
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.44
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.29
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.34
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.51
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.56
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.90
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.30
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.73
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.79
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.18
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.85
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.48
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.99
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.03
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.85
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.03
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.01
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.11
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.28
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.39
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.12
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.48
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.04
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.22
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.45
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.91
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.32
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:24.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.33
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:22.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.13

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.10e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.37e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.78
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.79
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.45
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:30.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.10
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:29.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.80
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10030.55
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.090
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:04:37.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5014.29
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:13.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.92
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:11.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4247.47
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:37.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11729.71
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11432.74
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.00
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000061939

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.26
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999947369

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:41.63

 All tests were passed




Server wird beendet - Lösche Semaphor 116097028.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5422
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:52.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4455
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:03.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7470
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:04.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7502
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:55.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:02.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    2.66
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     640
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:15.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.75
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.86
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:42.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.57
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.27
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.04
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.25
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.82
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.18
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.87
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:59.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7272.69
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.95
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.89
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:08.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.15
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.11
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.57
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:16.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45660
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869660
  j =  1                              :        399908685
  j =  2                              :            45650
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45508
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869508
  j =  1                              :        399908986
  j =  2                              :            45504
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:29.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:45.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:59.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:53.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:34.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.27e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.37e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.33
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.47
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.63
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.62
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:37.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.84
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.00
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.06
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17435.20
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.60
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.57
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.10
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.58
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.49
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   16.32
p-value of test                       :    0.9980


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.33
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.52
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.13
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.37
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.92
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.14
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.57
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.95
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.40
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.48
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.02
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.45
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.76
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.63
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.02
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5143.61
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.48
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.44
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.58
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.28
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4870.62
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.43
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.83
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:34.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.70
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -0.79
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:22.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.52
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   0.066
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:23.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.05e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 8.17e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.19e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 5.81e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.84
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.32
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.60
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  251.62
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.34
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:06.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.26
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10101.50
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.60
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:38.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  2.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4679.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:48.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.50
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.15
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11790.56
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.78
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.38
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999997964

Normal statistic for number of bits   :  -0.016
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.72
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000064936

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    2.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.91

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:41.48

 All tests were passed




Server wird beendet - Lösche Semaphor 117538820.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5472
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:53.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7486
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:04.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:58.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:04.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     336
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:13.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:43.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.61
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.44
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.27
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.78
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.66
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1356.51
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:05.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6825.76
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.64
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:10.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.39
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.03
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:37.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5198.35
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:01.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45866
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869866
  j =  1                              :        399908270
  j =  2                              :            45862
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45751
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869751
  j =  1                              :        399908502
  j =  2                              :            45743
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  6.0e-3

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:29.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.83e-3
p-value of test                       :    0.9902

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:18.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:02.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.76e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-5
p-value of test                       :    0.9940

Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:45.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.71
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.77
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.22
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.31
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.06
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.74
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.98
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17692.72
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.92
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.03
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.77
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.16
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.76
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.93
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.04
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.53
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.07
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.67
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.07
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.73
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.08
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.70
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.03
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.48
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.27
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.30
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.55
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.50
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.25
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.55
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.40
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  241.52
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.98
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.79
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.80
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.46
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:22.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.41
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    1.36
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:23.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.57e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 3.64e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.57
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.83
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.02
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:04.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.37
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:05.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10125.59
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.65
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:19.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.13
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:53.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.47
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:53.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4266.18
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4260.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11765.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11600.65
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:31.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.23
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000073132

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.08
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000056140

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:11.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:34.85

 All tests were passed




Server wird beendet - Lösche Semaphor 118456324.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5549
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:52.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:39.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:39.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7135
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:07.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:59.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:04.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.17
p-value of test                       :    0.9968

Test on the Nm values of W_{n,i}(mNP1):    2.06
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.85
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.14
p-value of test                       :  7.8e-3

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    3.22
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:14.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    3.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:41.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.36
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.83
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.85
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.94
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.58
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  390.57
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:51.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.07
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:09.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7259.09
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.91
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.11
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:08.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.96
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.45
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5136.72
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:58.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45674
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869674
  j =  1                              :        399908656
  j =  2                              :            45666
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45611
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869611
  j =  1                              :        399908782
  j =  2                              :            45603
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:28.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:15.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:02.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :  2.6e-4    *****

Anderson-Darling statistic = A2       :    5.10
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:36.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.049
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.69
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.40
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.81
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.13
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.96
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.48
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17536.85
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.54
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.40
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.12
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.68
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.73
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.05
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.18
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.70
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.93
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.53
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.15
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.43
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.30
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.10
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.87
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.40
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.47
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.07
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.09
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.11
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.44
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.69
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.64
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.10
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  314.35
p-value of test                       :    0.9961


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.88
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5161.65
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.65
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.24
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.70
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:21.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.32
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:23.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.12e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 7.78e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.84
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.38
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.74
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:04.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:04.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9952.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9804.94
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:04:15.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.40
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:53.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.65
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:53.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.06
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.21
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11724.03
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.91
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:30.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.00
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000008041

Normal statistic for number of bits   :   0.064
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.02
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000051544

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.34e-3
p-value of test                       :    0.9955

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:25.77

 All tests were passed




Server wird beendet - Lösche Semaphor 119570436.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:52.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:39.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7471
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:04.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:56.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:01.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    2.20
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    2.08
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:14.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:42.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.21
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.09
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.54
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.22
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.30
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.72
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  508.27
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1512.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6884.96
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.45
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.97
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:02.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.77
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.68
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:33.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4939.07
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:04.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45852
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869852
  j =  1                              :        399908299
  j =  2                              :            45846
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45805
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869805
  j =  1                              :        399908395
  j =  2                              :            45795
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:28.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:18.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-5
p-value of test                       : 1 -  1.3e-5    *****

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:59.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 5.58e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.59e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:35.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.14
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:48.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.29
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.63
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.83
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.33
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:37.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.28
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.86
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17577.94
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.18
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.53
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.71
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.60
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.72
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.67
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.20
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.96
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.78
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.47
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.47
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.69
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.53
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.24
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.56
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.93
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.80
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.33
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.38
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.20
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.37
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5179.16
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.03
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.99
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.86
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.08
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5211.86
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  432.67
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.22
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.55
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -2.87
p-value of test                       :    0.9980



-----------------------------------------------
CPU time used                    :  00:02:22.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.29
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:22.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.20
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.71e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 6.55e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.11
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.72
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.18
p-value of test                       :  7.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  150.35
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:02:05.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.30
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.96
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10271.70
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.080
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:39.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.38
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:51.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4224.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.15
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11835.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.44
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000060889

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.81
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000000223

Normal statistic for number of bits   : 1.76e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
p-value of test                       :    0.9909

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -2.03
p-value of test                       :    0.98

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.041
p-value of test                       :    0.52

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:29.14

 All tests were passed




Server wird beendet - Lösche Semaphor 120619012.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:55.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:42.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4200
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:01.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:10.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:11.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:10.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:15.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    2.45
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     262
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    3.21
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:15.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:41.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.64
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.45
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.72
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.11
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:29.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.11
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:58.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.40
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:07.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6907.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.85
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:17.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.76
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:47.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.08
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4992.85
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:04.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45789
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869789
  j =  1                              :        399908426
  j =  2                              :            45781
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908371
  j =  2                              :            45810
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:32.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:20.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:53.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.4e-3

Kolmogorov-Smirnov- statistic = D-    : 3.61e-3
p-value of test                       :    0.9961

Anderson-Darling statistic = A2       :    4.47
p-value of test                       :  5.3e-3


-----------------------------------------------
CPU time used                    :  00:02:11.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:38.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 9.43e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.81e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:54.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.12
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.23
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.69
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.01
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.64
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.15
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:12.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17265.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.05
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.09
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.29
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.66
p-value of test                       :    0.9952


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.06
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.19
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.69
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.46
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.33
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.89
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.53
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.08
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.25
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.54
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.15
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  575.57
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.97
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.95
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:40.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.90
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.88
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.14
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.07
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.55
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:33.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.23
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  306.80
p-value of test                       :    0.9985


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5155.36
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.84
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.13
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:33.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.64
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:13.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.37
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:15.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.10
p-value of test                       :    0.02

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.97e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:43.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.21
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.00
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.69
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.34
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:55.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.05
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10025.56
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:04:01.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:44.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.53
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.16
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11718.56
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.65
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.21
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999992573

Normal statistic for number of bits   :  -0.059
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.38
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000021112

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    2.73
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:45.65

 All tests were passed




Server wird beendet - Lösche Semaphor 121569284.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1508
p-value of test                       :  6.7e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334628
  j =  1                              :        599996984
  j =  2                              :             1508
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:41.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:36.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:34.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:53.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:54.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:00.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:00.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:53.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:58.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:50.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.81
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:10.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    6.76
p-value of test                       :  4.9e-4    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     121
p-value of test                       :    0.9916

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:37.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.92
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.30
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.42
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   39.42
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.99
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.51
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.07
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.49
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.43
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  544.18
p-value of test                       :  2.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1542.68
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:01.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7032.08
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:02.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.66
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.37
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4956.83
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:11.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46168
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870168
  j =  1                              :        399907665
  j =  2                              :            46166
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45481
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869481
  j =  1                              :        399909042
  j =  2                              :            45473
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:28.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:17.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:58.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:52.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:33.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.73e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.098
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.044
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.53
p-value of test                       :    0.9943

-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.71
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.12
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:41.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.21
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:32.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:31.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  160.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17521.25
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.65
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.46
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.98
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.56
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.03
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.03
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.06
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.36
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.74
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.97
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.24
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.72
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.90
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:48.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.11
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.05
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.03
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.85
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.51
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:47.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.04
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.66
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4830.62
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.70
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.56
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.76
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.04
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4888.50
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.32
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.76
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.65
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   -1.77
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:15.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.49
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:12.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:14.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.57e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:46.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.64
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.93
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.78
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:09.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.72
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:11.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10044.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9987.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:42.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.55
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.13
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.28
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11786.29
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11729.03
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.42
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999984620

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.75
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000054751

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   0.037
p-value of test                       :    0.49

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:33.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           6.7e-5
 25  ClosePairs NP, t = 16           4.9e-4
 35  Gap, r = 25                     2.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 102465563.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:42.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:36.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:34.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:53.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:55.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:01.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:01.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:53.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:56.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.86
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:12.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:38.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.20
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.73
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.63
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.90
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.79
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.80
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.90
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:06.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6954.34
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.93
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:08.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.69
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.76
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5037.22
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:05.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908204
  j =  2                              :            45889
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46008
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870008
  j =  1                              :        399907989
  j =  2                              :            45998
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:30.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:20.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:53.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:36.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.010
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.071
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.75
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.90
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.70
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.58
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.78
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.76
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.57
p-value of test                       :  6.8e-4    *****

Anderson-Darling statistic = A2       :    8.19
p-value of test                       :  1.0e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   78.45
p-value of test                       :  2.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.46
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:01:29.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:31.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.16
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17289.25
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.72
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.41
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.90
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.03
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.51
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.58
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.16
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.30
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.04
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.82
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.25
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.61
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.37
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.03
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.62
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.07
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.20
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.61
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.17
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.22
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.92
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.61
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.12
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.16
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.04
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4696.77
p-value of test                       :    0.9990


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.93
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.61
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.81
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:25.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.54
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    2.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 5.38e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.89e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.18
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.56
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.68
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:05.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.16
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:08.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.22
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9937.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:04:15.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.64
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:51.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.41
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:53.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.53
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11820.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:32.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11892.17
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:32.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.18
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999967949

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.17
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000019354

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:11.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:19.78
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 67  MatrixRank, L=30, r=26          2.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 102826011.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5567
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:47.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:37.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4486
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:55.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:04.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:04.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:59.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:05.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:15.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:42.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.81
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.07
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.74
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.62
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.20
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.00
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:55.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1547.68
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:07.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7081.71
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.02
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.63
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:19.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.36
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.89
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:39.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5008.38
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:57.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45775
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869775
  j =  1                              :        399908452
  j =  2                              :            45771
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45687
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869687
  j =  1                              :        399908628
  j =  2                              :            45683
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:30.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:16.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  8.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:07.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:37.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.72e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:51.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:51.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.60
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.04
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.63
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.05
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.26
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:51.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.0e-3

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.41
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.89
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17449.46
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.62
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.09
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.81
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.51
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.80
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.25
p-value of test                       :    0.9912


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.29
p-value of test                       :    0.9914


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.72
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.15
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.86
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.22
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.51
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.88
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.30
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.07
p-value of test                       :    0.9903


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.23
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.71
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.59
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.20
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.41
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.26
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.11
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.20
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.52
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.56
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.15
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.60
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.34
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.17
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:21.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.68
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    2.10
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:22.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.90e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.68
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.74
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.89
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:08.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.54
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:07.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10095.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9876.94
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:04:29.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.65
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5032.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:59.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3947.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.29
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12085.80
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:35.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11744.58
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.72
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999904463

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.15
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999965177

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.36
p-value of test                       :  9.2e-3

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:08.62

 All tests were passed




Server wird beendet - Lösche Semaphor 104169499.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1490
p-value of test                       :  4.1e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334610
  j =  1                              :        599997020
  j =  2                              :             1490
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5302
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:52.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:41.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:49.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:10.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:27.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:33.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:14.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7094
p-value of test                       :    0.9957


-----------------------------------------------
CPU time used                    :  00:04:51.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     839
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    3.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:13.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.93
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:43.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.44
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.75
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.35
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.86
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.80
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7162.71
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.73
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:04.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.20
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   83.29
p-value of test                       :    0.9947


-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4944.86
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:07.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45796
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869796
  j =  1                              :        399908410
  j =  2                              :            45792
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46018
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870018
  j =  1                              :        399907972
  j =  2                              :            46002
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.70e-3
p-value of test                       :    0.9944

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:36.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:33.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:02.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
p-value of test                       :    0.9932

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:24.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :  1.5e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 1.48e-3
p-value of test                       :    0.9984

Anderson-Darling statistic = A2       :    5.40
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:32.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.60
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.05
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.06
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:11.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.77
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.06
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:45.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.65
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.33
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.17
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:36.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17700.92
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.42
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.34
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.28
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.19
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.60
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.68
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.69
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.49
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.41
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.48
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.35
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.61
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   47.46
p-value of test                       :    0.9930


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.01
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.81
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.30
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.65
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.99
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.10
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.90
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.51
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.04
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.38
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.51
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4907.43
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.93
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.08
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.80
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:25.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.67
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:24.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 8.99e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.76e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.95
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.35
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.54
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:06.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.66
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:07.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9724.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10188.83
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:04:04.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.89
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:49.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.64
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:51.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4221.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3991.85
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12026.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11692.71
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:29.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.18
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000139207

Normal statistic for number of bits   :    1.10
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.55
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999956744

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.19
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:33.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  5  CollisionOver, t = 3            4.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 105381903.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5354
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:49.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:39.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:37.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4453
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4233
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:04.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:04.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:55.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:00.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.73
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.76
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.70
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.41
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.78
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.71
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.58
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:43.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1352.73
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7119.29
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.65
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:00.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.21
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.08
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:34.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5033.02
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:57.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45480
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869480
  j =  1                              :        399909042
  j =  2                              :            45476
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45718
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869718
  j =  1                              :        399908568
  j =  2                              :            45710
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:28.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:19.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 2.96e-3
p-value of test                       :    0.9969

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  9.8e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:55.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:32.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.61e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 8.43e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9957

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:35.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:35.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.87
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.66
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.84
p-value of test                       :    0.9943

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.23
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.35
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.97
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.23
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17611.34
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.10
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.17
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.49
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.48
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.46
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.56
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.01
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.19
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.29
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.04
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.29
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.38
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.93
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.47
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.65
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.64
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4867.09
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.42
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.70
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.51
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.53
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.31
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.39
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.84
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.65
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.94
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -1.80
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:25.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 7.41e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.81e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 4.45e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.92
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.57
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   40.00
p-value of test                       :  4.5e-3



-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.22
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:07.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.97
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:06.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.98
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9834.06
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.33
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:42.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.28
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.23
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.67
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11911.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.50
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.84
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999982709

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.25
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000037102

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   0.079
p-value of test                       :    0.47

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:01.35

 All tests were passed




Server wird beendet - Lösche Semaphor 106266639.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5499
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:49.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:38.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:37.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4190
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:55.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:04.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7064
p-value of test                       :    0.9986


-----------------------------------------------
CPU time used                    :  00:03:03.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:54.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:00.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9915

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:13.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:41.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.27
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.85
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.71
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.33
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.19
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1390.29
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7115.90
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.16
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.00
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:02.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.18
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.17
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:33.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.60
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:59.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45515
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869515
  j =  1                              :        399908973
  j =  2                              :            45509
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46011
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870011
  j =  1                              :        399907983
  j =  2                              :            46001
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:27.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:18.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:59.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:32.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:37.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.56
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:47.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.82
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.25
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.25
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:40.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.80
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17457.86
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.50
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.01
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.29
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.21
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.61
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.15
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.54
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.56
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.48
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.36
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.14
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.81
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.74
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.38
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.94
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.69
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.76
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.89
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.40
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.26
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.84
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.00
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.87
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.95
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.97
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.91
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.50
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:22.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.24
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:25.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.51e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.78e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.35
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.24
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.00
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:08.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:08.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9840.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10063.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:42.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.35
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5065.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.88
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11715.99
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11979.35
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.38
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999865607

Normal statistic for number of bits   :   -1.06
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.38
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999872237

Normal statistic for number of bits   :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:45.45

 All tests were passed




Server wird beendet - Lösche Semaphor 107282447.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:48.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:38.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7154
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:37.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7594
p-value of test                       :  6.9e-4    *****


-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:03.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:54.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:04:00.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     849
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9915

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:13.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.48
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:40.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.38
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.76
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.35
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.04
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.51
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.76
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1335.01
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7193.54
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.04
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.45
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:00.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.32
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.28
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5138.00
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:03.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46093
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870093
  j =  1                              :        399907820
  j =  2                              :            46081
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46395
p-value of test                       :  8.2e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870395
  j =  1                              :        399907214
  j =  2                              :            46387
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:28.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:19.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9944

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:33.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.87e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.72e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.091
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.84
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.48
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.06
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.40
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.51
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:37.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.23
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   66.04
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17087.23
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.26
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.85
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.39
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.87
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.68
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.19
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.05
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.64
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.95
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.55
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.57
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  193.42
p-value of test                       :  5.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.07
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.50
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.46
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.45
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.73
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.75
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.90
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.79
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.77
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5222.09
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.81
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.19
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.61
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.01
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.99
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.84
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.66
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.28
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    1.39
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:23.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.43
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    2.09
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:25.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 8.48e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.60
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.53
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.13
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:06.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.72
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:07.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10225.27
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9798.93
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.075
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : -7.89e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:42.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4760.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.89
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.06
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.79
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12016.15
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11778.59
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.51
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000003211

Normal statistic for number of bits   :   0.025
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.55
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000052045

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.75
p-value of test                       :    0.96

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:31.32
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 18  BirthdaySpacings, t = 8         6.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 108298255.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1239
p-value of test                       :    0.9997    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334359
  j =  1                              :        599997522
  j =  2                              :             1239
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:50.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:38.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:38.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:03.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:02.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:56.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:58.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    2.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:12.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:39.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.66
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.20
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.89
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.76
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:38.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.44
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:38.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.23
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:45.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.14
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:05.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7146.92
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.09
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.68
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.09
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.65
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:35.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5083.00
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:10.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46193
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870193
  j =  1                              :        399907615
  j =  2                              :            46191
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45567
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869567
  j =  1                              :        399908867
  j =  2                              :            45565
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:28.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979


-----------------------------------------------
CPU time used                    :  00:02:20.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:47.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:36.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.35e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 6.90e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.65e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:39.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:48.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.65
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.68
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.60
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.12
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.78
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:45.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.37
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.58
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.94
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17319.00
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.24
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.80
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.46
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.81
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.82
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.73
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.30
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.96
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.19
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.67
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.66
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.48
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.13
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.17
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.03
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.32
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.39
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.71
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.06
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.95
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.07
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.79
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.17
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.42
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4817.86
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.39
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.78
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.85
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.41
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:25.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.99e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 6.25e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.23
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.11
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.52
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:07.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.12
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10117.07
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9874.18
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:52.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.30
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.77
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:51.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.01
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.25
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11697.69
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11672.20
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:31.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.33
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000076954

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.02
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999998417

Normal statistic for number of bits   :  -0.013
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   0.091
p-value of test                       :    0.46

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:54.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 109248527.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5481
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:54.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4566
p-value of test                       :  2.9e-4    *****


-----------------------------------------------
CPU time used                    :  00:01:59.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:59.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7515
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:08.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:09.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:08.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:13.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    2.39
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    3.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    3.33
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    3.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.88
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:11.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.81
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:38.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.64
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.49
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.07
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.59
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.10
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.13
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:58.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.84
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:06.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7278.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:58.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.70
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:21.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.05
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:47.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.14
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5041.41
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:02.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45852
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869852
  j =  1                              :        399908300
  j =  2                              :            45844
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45760
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869760
  j =  1                              :        399908485
  j =  2                              :            45750
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:32.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:20.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:54.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:12.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-5
p-value of test                       :    0.9958

Kolmogorov-Smirnov- statistic = D-    : 2.74e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:24.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:51.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:52.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.27
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.52
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.58
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.95
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:53.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.98
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.46
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.49
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17556.88
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.87
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.95
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.81
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.66
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.25
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.82
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.98
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.10
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.87
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.66
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.28
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.26
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.39
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.24
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.52
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.71
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.58
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.22
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.84
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4794.73
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.97
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.03
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.36
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.32
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5076.39
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.75
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.75
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.62
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:25.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.57
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:23.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.33e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.38e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 9.52e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.07
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.05
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.00
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:04.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.59
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.83
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.30
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10315.89
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:04:33.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4956.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:54.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.69
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.07
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4243.33
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11730.87
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:36.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:38.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.31
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000002404

Normal statistic for number of bits   :   0.019
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.68
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000040597

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.86e-3
p-value of test                       :    0.9904

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.75
p-value of test                       :  4.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.08
p-value of test                       :  1.0e-3

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         : 8.38e-3
p-value of test                       :    0.50

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:07.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 16  BirthdaySpacings, t = 7         2.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 110198799.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:51.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:39.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:39.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:57.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:05.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:04.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:54.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:58.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:45.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.98
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     557
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.57
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:12.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.31
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:42.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.90
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.34
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.62
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.59
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.27
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.35
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:08.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7176.74
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:46.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
p-value of test                       :    0.9919

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   49.62
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:05.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.33
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.71
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:36.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4881.88
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:58.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45562
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869562
  j =  1                              :        399908877
  j =  2                              :            45560
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45616
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869616
  j =  1                              :        399908772
  j =  2                              :            45608
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:28.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:16.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:44.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  8.0e-3

Kolmogorov-Smirnov- statistic = D-    : 9.83e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    6.01
p-value of test                       :  1.0e-3

-----------------------------------------------
CPU time used                    :  00:01:35.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.21e-6
p-value of test                       :    0.9973

Kolmogorov-Smirnov- statistic = D-    : 2.69e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:39.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:50.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.92
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.94
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.30
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:44.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.10
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.54
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.86
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.84
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 6.21e-3
p-value of test                       :    0.9934

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17735.44
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.17
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.39
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.26
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.00
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.78
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.57
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.77
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.47
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.49
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.20
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.16
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.72
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.52
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.53
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.45
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.18
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.97
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.14
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.15
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.32
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.22
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.91
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.78
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.14
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.12
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.49
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5090.47
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.58
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.06
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.61
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:21.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.98
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:24.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.74
p-value of test                       :    0.04

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 5.92e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.27
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.80
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.61
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:07.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:09.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10085.42
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9789.21
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:04:05.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.22
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5025.91
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.31
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11725.19
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11597.35
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.33
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000025246

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.56
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000020632

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:02.12

 All tests were passed




Server wird beendet - Lösche Semaphor 111378447.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:40.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5539
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:52.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:04.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:57.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:02.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:14.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:42.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.97
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.02
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.37
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.84
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.88
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1401.35
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:03.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6927.12
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.70
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.59
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.01
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.23
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:29.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5002.09
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:56.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46017
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870017
  j =  1                              :        399907969
  j =  2                              :            46011
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45612
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869612
  j =  1                              :        399908778
  j =  2                              :            45608
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9970


-----------------------------------------------
CPU time used                    :  00:02:27.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  7.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.36
p-value of test                       :  6.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9962


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:18.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9918


-----------------------------------------------
CPU time used                    :  00:02:00.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:32.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.70
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:48.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.11
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:38.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.19
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.50
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.79
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.59
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9965

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17407.60
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.74
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.62
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.79
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.43
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.17
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.40
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.12
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.02
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.66
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.68
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.16
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.38
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.14
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.24
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.19
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.36
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.72
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.61
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.75
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.41
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.90
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4763.14
p-value of test                       :    0.9918


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.73
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.10
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.21
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.84
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.61
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.18
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.27
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.90
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.97
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:21.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.81e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.02e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 7.04e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.67
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.34
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.82
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.08
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:07.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9848.71
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.60
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:45.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.05
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4198.19
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3967.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11836.33
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.03
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.61
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000002008

Normal statistic for number of bits   :   0.016
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.90
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000197218

Normal statistic for number of bits   :    1.56
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         : -6.64e-3
p-value of test                       :    0.50

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.5e-3

Anderson-Darling statistic = A2       :    4.36
p-value of test                       :  6.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.42
p-value of test                       :  7.8e-3

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:17.25

 All tests were passed




Server wird beendet - Lösche Semaphor 112459791.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9924


-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5231
p-value of test                       :    0.9952


-----------------------------------------------
CPU time used                    :  00:03:51.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7172
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:57.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:05.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:05.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:54.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:01.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:11.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.72
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:41.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.41
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.64
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.11
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.03
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6985.83
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.81
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.15
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:01.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.85
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:35.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4995.35
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:03.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45883
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869883
  j =  1                              :        399908238
  j =  2                              :            45875
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45992
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869992
  j =  1                              :        399908023
  j =  2                              :            45978
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:29.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:18.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:33.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.48e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.84
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:47.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.54
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.00
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.00
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:38.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.07
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.93
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17043.94
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.02
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.20
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.39
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.09
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.12
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.87
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.06
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.53
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.00
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.06
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.37
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.22
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.21
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.78
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.78
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.50
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.54
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.96
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.47
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.75
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.74
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.60
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.16
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.67
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.16
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.57
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.99
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.84
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.90
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :   -1.29
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.40
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:27.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.01e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 6.12e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 9.81e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.05
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.01
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.00
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:07.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:06.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10082.36
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.57
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.081
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:45.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.80
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:49.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.03
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11823.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11979.81
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.40
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000302503

Normal statistic for number of bits   :    2.39
p-value of test                       :  8.4e-3



-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.11
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999910586

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:19.90

 All tests were passed




Server wird beendet - Lösche Semaphor 113344527.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5581
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:52.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:39.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:03.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:54.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:00.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.99
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    5.73
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:11.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.74
p-value of test                       :  4.3e-3

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:41.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.67
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.48
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.09
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.77
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.47
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.73
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.72
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.74
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6944.17
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.90
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.58e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   87.91
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:02.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.95
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.55
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:32.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5004.28
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:01.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45571
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869571
  j =  1                              :        399908864
  j =  2                              :            45559
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46015
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870015
  j =  1                              :        399907971
  j =  2                              :            46013
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:28.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9961

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.80e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.020
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:39.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.40
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.94
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.25
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.96
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.05
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:37.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.34
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.76
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17293.27
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.01
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.97
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.33
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.26
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.07
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.24
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.08
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.94
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.79
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.00
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.00
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.95
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.46
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.17
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.45
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.17
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.10
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.35
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.28
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.81
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.85
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.30
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.78
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.19
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.93
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.54
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.22
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.99
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.02
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.04
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.68
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:22.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.33
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:25.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.56e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.66e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.73
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.60
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.52
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:07.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.33e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.6e-3

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  257.41
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:02:08.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.08
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9774.08
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:42.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:48.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4741.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:50.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.80
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.22
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:29.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.29
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999896567

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.56
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000008704

Normal statistic for number of bits   :   0.069
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.17
p-value of test                       :    0.98

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :  -0.100
p-value of test                       :    0.54

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:24.10

 All tests were passed




Server wird beendet - Lösche Semaphor 114327567.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1490
p-value of test                       :  4.1e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334610
  j =  1                              :        599997020
  j =  2                              :             1490
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5289
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:52.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:05.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:05.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:57.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     948
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:13.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9958


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.92
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:38.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.75
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.95
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.59
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.08
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.94
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.25
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.32
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1406.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:04.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7010.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:08.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.98
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.88
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:36.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4960.96
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:58.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45464
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869464
  j =  1                              :        399909079
  j =  2                              :            45450
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46024
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870024
  j =  1                              :        399907954
  j =  2                              :            46020
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:29.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:18.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:03.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 9.57e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:43.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.09
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.55
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.32
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.27
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.57
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17520.93
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.51
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.51
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.59
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.34
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.84
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.83
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.11
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   44.11
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.99
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.95
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.26
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.42
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.97
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.17
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.66
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.13
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.35
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.53
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.01
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.89
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.72
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  461.10
p-value of test                       :  4.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.25
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.66
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.32
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.52
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.21
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.07
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.53
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.66
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.08
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:24.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.91
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -1.90
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:23.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    2.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.68e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 5.36e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.53
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.71
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.58
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:04.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.1e-3

Anderson-Darling statistic = A2       :    4.67
p-value of test                       :  4.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  250.08
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:02:06.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.11
p-value of test                       : 1 -  9.4e-5    *****

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.73
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10148.51
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:04:16.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:53.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.08
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:53.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4227.62
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.48
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11635.30
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11902.69
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.70
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999928580

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.78
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999988871

Normal statistic for number of bits   :  -0.088
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9949

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   0.014
p-value of test                       :    0.49

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:18.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           4.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 115310607.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:53.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7462
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:04.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:03.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:54.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:00.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.93
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:12.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:42.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.29
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.92
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.23
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.46
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.36
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.83
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  300.77
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.26
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.91
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6978.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:43.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:02.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.63
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.53
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4882.55
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:04.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46029
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870029
  j =  1                              :        399907947
  j =  2                              :            46019
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45960
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869960
  j =  1                              :        399908084
  j =  2                              :            45952
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  7.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:29.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:18.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:54.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:34.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.80e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.83e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:35.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.40
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.15
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.35
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.57
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.32
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.89
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.81
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.61
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.64
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17206.38
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.93
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.37
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.88
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.67
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.16
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.64
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.23
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.09
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.56
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.30
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.97
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.93
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.19
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.05
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.91
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.54
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.28
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.26
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.03
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4897.27
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.50
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.02
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.50
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.80
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.18
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.31
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  255.96
p-value of test                       :  4.6e-3


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.00
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:24.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.76
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:23.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 5.18e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.62e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.91
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.38
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.16
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:07.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.20
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:06.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10219.18
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.89
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:46.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.58
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4743.95
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:51.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.12
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.78
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11718.32
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11868.81
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.82
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000038506

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.60
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999981416

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.74
p-value of test                       :    0.04

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:37.07

 All tests were passed




Server wird beendet - Lösche Semaphor 116424719.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5415
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:53.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4199
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:40.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:04.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:03.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:54.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.86
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    3.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.02
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.97
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:13.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    2.35
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:43.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.66
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.68
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.80
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.61
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  269.11
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.21
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7099.60
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:41.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.05
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.99
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:02.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.64
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.91
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:35.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5124.23
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:58.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45884
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869884
  j =  1                              :        399908238
  j =  2                              :            45872
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45674
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869674
  j =  1                              :        399908657
  j =  2                              :            45664
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:28.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9937


-----------------------------------------------
CPU time used                    :  00:02:19.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:00.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 7.11e-3
p-value of test                       :    0.9906

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:32.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.16e-6
p-value of test                       :    0.9979

Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.91e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.74e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:29.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.14
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.73
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.70
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.88
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.27
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.85
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.61
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.52
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17511.09
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.77
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.97
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   44.95
p-value of test                       :  5.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.09
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.05
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.19
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.90
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.36
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.88
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.94
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.90
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  439.01
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.16
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.90
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.67
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.17
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.92
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.12
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.67
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.77
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.14
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.83
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.12
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.86
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.51
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.65
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.51
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.57
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.52
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:25.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.00
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:25.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   0.043
p-value of test                       :    0.48

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 2.47e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 7.72e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.47
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.92
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.64
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:04.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9885.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9958.79
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:42.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.11
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.95
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:50.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.63
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.07
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12067.23
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11585.28
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:30.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.51
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999924173

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.98
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000088147

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:58.15

 All tests were passed




Server wird beendet - Lösche Semaphor 117342223.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:53.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:03.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:03.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:54.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:00.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9928


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:14.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.44
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:45.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.84
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.67
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.44
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.74
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.83
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  272.38
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  473.71
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.31
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7083.28
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.50
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.16
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:04.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.19
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.47
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.04
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:54.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46167
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870167
  j =  1                              :        399907669
  j =  2                              :            46161
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45862
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869862
  j =  1                              :        399908282
  j =  2                              :            45850
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:28.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:19.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:45.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:32.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.37e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:34.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.00
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.14
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.07
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.67
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:37.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.40
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.58
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.40
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17649.15
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.41
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.45
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.70
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.50
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.82
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.63
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.80
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.29
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.78
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.31
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.41
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.49
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.84
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.86
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.58
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.42
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.69
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.02
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.47
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.41
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5161.19
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.08
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.76
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.48
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.16
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5150.11
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.84
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.93
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:34.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.55
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   0.070
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:23.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.29
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :   0.021
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:24.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.15e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 9.73e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.87
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.39
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:06.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:05.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10278.69
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10025.63
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:40.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.85
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:48.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.51
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:50.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.63
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.58
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11929.85
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11942.11
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.39
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000027490

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.06
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999844397

Normal statistic for number of bits   :   -1.23
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-3
p-value of test                       :    0.9988

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.85
p-value of test                       :    0.03

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.028
p-value of test                       :    0.51

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    2.62
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:23.86

 All tests were passed




Server wird beendet - Lösche Semaphor 118325263.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:48.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5319
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:55.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4194
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:05.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:04.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:57.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:00.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    2.47
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     836
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9950


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.46
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:13.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:40.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.80
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.12
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.99
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.58
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.59
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.44
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.30
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.68
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.20
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:06.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6977.01
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.95
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.84
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:08.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.50
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5118.20
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:59.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869892
  j =  1                              :        399908219
  j =  2                              :            45886
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45164
p-value of test                       :    0.9996    *****


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869164
  j =  1                              :        399909675
  j =  2                              :            45158
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.43e-3
p-value of test                       :    0.9933

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:30.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:19.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:35.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:41.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:41.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.99
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.66
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.11
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.03
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17573.75
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.58
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.74
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.05
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.09
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.21
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.60
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.41
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.33
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.22
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.55
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.88
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.40
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.52
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.89
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.46
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.74
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.79
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.65
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.75
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.73
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.07
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.30
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.49
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.16
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.71
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.84
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.67
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.27
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.85
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:25.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.20
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    1.35
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:24.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 6.68e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.31
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.95
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:05.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.46
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:05.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.78
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.06
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.065
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:04:17.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9934

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:52.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4993.51
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:53.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.51
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.27
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12054.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.12
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:31.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.12
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999893537

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.84
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999998858

Normal statistic for number of bits   : -9.03e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:11.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:27.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 45  CollisionPermut, r = 10         0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 119275535.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1255
p-value of test                       :    0.9986

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334375
  j =  1                              :        599997490
  j =  2                              :             1255
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:56.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:08.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:07.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:03.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:04.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:13.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.73
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.88
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.35
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.44
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.92
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.74
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:50.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1498.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:06.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7087.12
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.46
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.99
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.28
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.92
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:38.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4998.47
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:00.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45681
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869681
  j =  1                              :        399908640
  j =  2                              :            45677
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45707
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869707
  j =  1                              :        399908590
  j =  2                              :            45699
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:32.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:21.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:51.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:07.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 8.01e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:42.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:43.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.41
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.58
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.03
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.61
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.52
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.45
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17460.69
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.66
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.37
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.41
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.20
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   16.66
p-value of test                       :    0.9976


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   13.27
p-value of test                       :    0.9997    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.13
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.09
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.01
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.91
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.47
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.55
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.47
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.01
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.66
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.80
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.47
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.59
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.50
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.43
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.29
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5105.09
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.94
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.50
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.96
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.35
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5118.59
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.97
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.02
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.98
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:24.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.21
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:24.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.59e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 8.61e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.05
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.25
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:06.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.11
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10169.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:04:22.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.50
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:54.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9933

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.97
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:58.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.02
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4263.29
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11483.15
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11967.96
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:34.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.22
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000055201

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.85
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000024097

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :  -0.057
p-value of test                       :    0.52

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:52.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 M (L=50, r=25)      0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 120455183.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:53.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4207
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:57.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:04.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:04.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:56.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7120
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:04:02.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:14.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9937

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     120
p-value of test                       :    0.9934

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:48.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.39
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.05
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.09
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.80
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.65
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.24
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.65
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:43.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.37
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6953.44
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:41.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.1e-3

Anderson-Darling statistic = A2       :    4.27
p-value of test                       :  6.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   88.04
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:01.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.23
p-value of test                       :    0.9987


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.14
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.90
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:58.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45740
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869740
  j =  1                              :        399908524
  j =  2                              :            45732
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45809
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869809
  j =  1                              :        399908385
  j =  2                              :            45803
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:27.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:19.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:56.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:33.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.33e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 3.10e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.33e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.50
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:33.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.67
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.97
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.59
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:41.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.06
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  100.33
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.3e-3

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17670.57
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.37
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.16
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.22
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.64
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.15
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.42
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.58
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.47
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.55
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.61
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.36
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.02
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.32
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.42
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.30
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.64
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.99
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.04
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.13
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.01
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.60
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4701.24
p-value of test                       :    0.9988


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.84
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.47
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.60
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.77
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.84
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.70
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.92
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.48
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -1.67
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:17.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.36
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:16.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.12
p-value of test                       :    0.02

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.35e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.78e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.90
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.05
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.83
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:58.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.88
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:57.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.099
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:24.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.76
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:39.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.07
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:30.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4015.96
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.60
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.88
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11740.86
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.60
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000061369

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.30
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000180991

Normal statistic for number of bits   :    1.43
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:58:33.87

 All tests were passed




Server wird beendet - Lösche Semaphor 121536527.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:51.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5447
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:41.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:36.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:34.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:53.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:54.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7094
p-value of test                       :    0.9957


-----------------------------------------------
CPU time used                    :  00:03:00.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:01.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:52.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7045
p-value of test                       :    0.9993    *****


-----------------------------------------------
CPU time used                    :  00:03:58.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    2.00
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:08.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.94
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:37.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.58
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.25
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.20
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.01
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.76
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.88
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.85
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:01.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7185.25
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:01.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.24
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:36.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5005.87
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:00.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45570
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869570
  j =  1                              :        399908863
  j =  2                              :            45564
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45792
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869792
  j =  1                              :        399908421
  j =  2                              :            45782
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:28.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 8.20e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:17.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:46.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:52.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:33.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.97e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 6.73e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.43
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.88
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.98
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.59
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.47
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:32.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.65
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17176.04
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.58
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.77
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.33
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.25
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.99
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.06
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.77
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.31
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.79
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.18
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.62
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.29
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.59
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.05
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.36
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  592.44
p-value of test                       :  2.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.84
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.42
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:47.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.89
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  450.89
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5115.24
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.15
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.46
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.97
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.10
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.53
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.75
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.41
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.24
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:14.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.01
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:12.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.76e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:47.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:46.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.45
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.59
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:10.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.80
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:11.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10028.24
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.61
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:56.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5037.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4719.15
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.32
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11947.65
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11994.76
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:30.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.13
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999994067

Normal statistic for number of bits   :  -0.047
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.75
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999972632

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.84
p-value of test                       :    0.03

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:50.03
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 21  BirthdaySpacings, t = 16        0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 102498332.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5462
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:43.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4218
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:35.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:01.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:01.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:53.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:58.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:09.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    2.37
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:36.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.70
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.26
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.11
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.15
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.34
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  276.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  482.76
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1355.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:02.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7113.61
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.73
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.08
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:04.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.93
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.10
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5243.71
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:58.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45878
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869878
  j =  1                              :        399908247
  j =  2                              :            45872
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45856
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869856
  j =  1                              :        399908297
  j =  2                              :            45838
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:29.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:18.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:45.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.47e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:34.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:35.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.07
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   39.77
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.74
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.55
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.77
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17464.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.86
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.92
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.35
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.70
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.96
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.44
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.41
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.81
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.39
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.71
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.23
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.13
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.94
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.73
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.40
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.26
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.89
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.74
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.35
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.99
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.86
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.85
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5118.79
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.78
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.40
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:34.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.40
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.99
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.68
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.10
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.89
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:34.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.64
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:17.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.04
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:20.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   0.043
p-value of test                       :    0.48

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 6.76e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.79e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.20
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.35
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.28
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:09.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.37
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:06.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.34
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.83
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.046
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:57.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5027.45
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.91
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4258.64
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11494.52
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.27
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.58
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999817841

Normal statistic for number of bits   :   -1.44
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.51
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999936074

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :  -0.075
p-value of test                       :    0.53

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:16.27

 All tests were passed




Server wird beendet - Lösche Semaphor 103219228.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:41.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:44.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:36.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:36.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:53.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:01.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:02.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:52.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:57.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    2.21
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     853
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.19
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.21
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     334
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:09.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.48
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.21
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.03
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  262.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.63
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1330.57
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7014.80
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:41.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:04.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.61
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:47.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.13
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4989.07
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:56.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46191
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870191
  j =  1                              :        399907621
  j =  2                              :            46185
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45618
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869618
  j =  1                              :        399908764
  j =  2                              :            45618
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:28.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:17.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:00.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:54.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.44e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.60e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 7.30e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.49
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.93
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.79
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.80
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.48
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.95
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.22
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.33
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17103.28
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.03
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.82
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.99
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   38.89
p-value of test                       :  1.8e-3


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.03
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.93
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.40
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.68
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.64
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.06
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.83
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.07
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.38
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.75
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.48
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.74
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.65
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.69
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.43
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4859.05
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.58
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.87
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.99
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.52
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  434.52
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.55
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:34.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.35
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:20.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.31
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:22.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.45e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.34e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.25
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.49
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:05.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.68
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:07.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.31
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.041
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.029
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:47.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.34
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4736.50
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3924.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.00
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.65
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12009.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.72
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000037501

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.68
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000091273

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:18.04

 All tests were passed




Server wird beendet - Lösche Semaphor 104071196.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:47.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:38.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:38.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:02.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:02.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7155
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:52.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:58.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    4.39
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:15.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:42.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.10
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.75
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.88
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.86
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.86
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:02.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7125.18
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.94
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:05.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.22
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   93.39
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5066.68
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:58.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45701
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869701
  j =  1                              :        399908600
  j =  2                              :            45697
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45943
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869943
  j =  1                              :        399908115
  j =  2                              :            45941
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:27.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:17.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:59.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:33.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.03e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.035
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:32.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.82
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.76
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.81
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.14
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.91
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.66
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.74
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.64
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.14
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.56
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17507.89
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.60
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.75
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.48
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.06
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.84
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.73
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.25
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.89
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.91
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.73
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.09
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.49
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.59
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.52
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.00
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.79
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  563.01
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.96
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.40
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.92
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.78
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.47
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.79
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.50
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.35
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.98
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4836.87
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.73
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.57
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.18
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:19.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.19
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   0.016
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:20.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.89e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 3.71e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.24
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.90
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:05.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.01
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9816.36
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:44.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.23
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.30
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11577.32
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.22
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:29.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.18
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000030127

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.93
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000061252

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:00.28

 All tests were passed




Server wird beendet - Lösche Semaphor 104923164.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:55.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:41.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4518
p-value of test                       :  3.2e-3


-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:03.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:02.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:54.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:56.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.16
p-value of test                       :    0.9979

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    3.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:15.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:47.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.55
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.30
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.64
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.70
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.81
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.14
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  166.61
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.65
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.32
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7165.84
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.58
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:08.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.58
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.34
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5145.26
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:56.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45798
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869798
  j =  1                              :        399908405
  j =  2                              :            45796
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46122
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870122
  j =  1                              :        399907759
  j =  2                              :            46116
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:29.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:02.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.53e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.68e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.092
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:41.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.44
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.02
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.94
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.66
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.36
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.12
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:46.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.02
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.79
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17416.91
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.11
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.71
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.03
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.36
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.57
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.39
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.48
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.13
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.89
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.83
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.56
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.60
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.58
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.95
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.14
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.93
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.19
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.18
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.62
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.19
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.67
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  445.18
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.35
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4904.31
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.47
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.29
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.44
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:25.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.31
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : 7.45e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:24.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.09
p-value of test                       :    0.98

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 7.94e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 9.56e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.04
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.26
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.05
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.96
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:04.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10004.92
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.92
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:04:21.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.94
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:52.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.23
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:54.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.71
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12269.69
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:01:31.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11998.83
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:31.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.53
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999988190

Normal statistic for number of bits   :  -0.093
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.10
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999906533

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:24.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 34  Gap, r = 0                      0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 105906204.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997185
  j =  2                              :             1406
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5447
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:56.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:38.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:55.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:03.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:54.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:00.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.87
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:12.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:43.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.67
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.61
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.58
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.09
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.72
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.55
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.49
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.64
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1499.91
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:06.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7113.78
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.57
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.96
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:08.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.31
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.46
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:37.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4907.88
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:00.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46088
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870088
  j =  1                              :        399907828
  j =  2                              :            46080
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45629
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869629
  j =  1                              :        399908747
  j =  2                              :            45619
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:29.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:18.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:45.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:02.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.21e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.30e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.18
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.37
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.11
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.42
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.16
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.37
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.78e-4
p-value of test                       :    0.9997    *****

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  171.95
p-value of test                       :  8.1e-3

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17659.74
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.40
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.98
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.88
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.56
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.87
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.07
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.30
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.24
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.03
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.03
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.81
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  559.68
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.15
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.82
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.10
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.92
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.25
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.98
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.34
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.64
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.56
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4840.96
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.98
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.33
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.69
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.60
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.23
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.23
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.47
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.66
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    1.43
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:24.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.55
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:24.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.36e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.93e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 5.44e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.85
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.97
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:06.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.71
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:06.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9772.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.75
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:04:19.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.82
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:53.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4990.90
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.98
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.35
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11939.83
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:31.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.42
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:31.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.10
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000006892

Normal statistic for number of bits   :   0.054
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.85
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000006412

Normal statistic for number of bits   :   0.051
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.075
p-value of test                       :    0.53

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:00.21

 All tests were passed




Server wird beendet - Lösche Semaphor 106922012.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5387
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:51.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:38.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:38.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:54.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:01.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:02.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:56.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:56.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.17
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:11.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.00
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:39.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.23
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.53
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.43
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.19
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.66
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.05
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:44.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:05.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7057.67
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.51
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:06.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.11
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5030.60
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:54.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45654
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869654
  j =  1                              :        399908695
  j =  2                              :            45648
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45985
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869985
  j =  1                              :        399908032
  j =  2                              :            45981
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:28.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:18.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:00.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:36.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 7.51e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 5.24e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:37.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.89
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.00
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.75
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.11
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.6e-3

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17074.80
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.19
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.94
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.56
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.91
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.96
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.52
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.87
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.33
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.39
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.36
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.35
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.39
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.96
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.47
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.08
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.86
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.20
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.02
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.51
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.23
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.45
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.66
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.42
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.47
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.22
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  444.46
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.74
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.30
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:20.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.91
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.06e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.22e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.16
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.28
p-value of test                       :    0.9958

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  248.98
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:07.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.6e-3

Anderson-Darling statistic = A2       :    4.94
p-value of test                       :  3.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  257.27
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:02:07.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9869.76
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9776.86
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:04:08.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.69
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.06
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.68
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11760.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11797.62
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:30.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.48
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999813674

Normal statistic for number of bits   :   -1.47
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.67
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000144712

Normal statistic for number of bits   :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:45.92

 All tests were passed




Server wird beendet - Lösche Semaphor 108101660.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:50.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5443
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:53.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:41.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:58.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:00.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:10.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:11.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:07.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:13.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    3.95
p-value of test                       :  9.2e-3

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     557
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:39.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.22
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.23
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.87
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.52
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.05
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.96
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:58.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:04.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7035.41
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.18
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.11
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:12.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.49
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:47.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.15
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5103.39
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:53.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45917
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869917
  j =  1                              :        399908174
  j =  2                              :            45901
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45954
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869954
  j =  1                              :        399908095
  j =  2                              :            45948
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:30.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:20.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:54.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:09.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:39.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 2.85e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.082
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:25.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:46.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.50
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:01:52.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.64
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.91
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.62
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.78
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.54
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:51.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.66
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.44
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17628.95
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.95
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.43
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.87
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.48
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.60
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.14
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.85
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.57
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.40
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.50
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.95
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.90
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.42
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.75
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.25
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.58
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.68
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.11
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.38
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.75
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.32
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.17
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.98
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  156.78
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.64
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.01
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.28
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.35
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  246.72
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   34.96
p-value of test                       :  4.8e-4    *****


-----------------------------------------------
Normal statistic for number of jumps  :   -2.64
p-value of test                       :    0.9958



-----------------------------------------------
CPU time used                    :  00:02:24.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.52
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:24.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.55
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.39
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.73e-3
p-value of test                       :    0.9940

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  160.91
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:07.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.85
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:14.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.63
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9701.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:04:41.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.77
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:52.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.67
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4023.61
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.31
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11560.09
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:33.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.89
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:36.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.52
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999995036

Normal statistic for number of bits   :  -0.039
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.83
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999984296

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:16.30
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0               4.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 109215772.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5423
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:50.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:39.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:07.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:06.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:57.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:59.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.14
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:13.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:42.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.75
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.46
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.89
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.28
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1496.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:06.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7169.20
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:07.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.60
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.50
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4939.60
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:11.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45837
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869837
  j =  1                              :        399908330
  j =  2                              :            45829
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45994
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869994
  j =  1                              :        399908016
  j =  2                              :            45986
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:28.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:17.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.37
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.03
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.02
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.69
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  162.18
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17316.02
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.64
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.11
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.85
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.51
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.86
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.40
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.88
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.43
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.67
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.61
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.90
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   97.88
p-value of test                       :    0.9943


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.04
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.52
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.07
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.40
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.07
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.85
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.32
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.66
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5253.36
p-value of test                       :  6.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.41
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.38
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.69
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.87
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4808.41
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.53
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.83
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.32
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -1.91
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.68
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:25.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 6.22e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.90
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.53
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.49
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:08.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.54
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:08.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9872.14
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9832.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.059
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:04:09.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:51.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.61
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:51.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3928.95
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4051.20
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11528.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11976.76
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.24
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999968816

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.91
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999994844

Normal statistic for number of bits   :  -0.041
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:16.77

 All tests were passed




Server wird beendet - Lösche Semaphor 110526492.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5485
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:52.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:41.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:05.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7501
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:58.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:02.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    3.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:16.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.10
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:45.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.16
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.80
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.52
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.41
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.98
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.62
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.79
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.16
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:06.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7010.41
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:10.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.87
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.70
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:37.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5034.63
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:12.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908371
  j =  2                              :            45810
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45823
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869823
  j =  1                              :        399908359
  j =  2                              :            45813
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.70e-3
p-value of test                       :    0.9929

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:29.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:19.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:05.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.86e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.073
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.04
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.36
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.31
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.49
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17478.85
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.86
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.91
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.65
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.68
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.06
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.69
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.39
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.08
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.56
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.75
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.06
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.61
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.52
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.95
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.68
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.37
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.77
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.69
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.90
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5069.14
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.35
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.55
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.75
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.58
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.75
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.48
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.97
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.15
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:25.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.95
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:25.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9925

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.14e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.80e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.47
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.64
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.50
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:05.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9783.04
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10004.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.032
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:04:10.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:52.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:52.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.30
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.94
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11951.40
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12050.41
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.62
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000097387

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.24
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999929366

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    2.73
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:40.21

 All tests were passed




Server wird beendet - Lösche Semaphor 111443996.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:41.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:53.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4456
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4453
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:04.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:05.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:02.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     845
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    2.86
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:14.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:40.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.14
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.46
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.46
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.10
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.59
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.86
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.17
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.33
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.94
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1539.15
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:59.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7158.70
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:42.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.20
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:02.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.10
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.02
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5045.76
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:10.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45951
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869951
  j =  1                              :        399908102
  j =  2                              :            45943
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45972
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869972
  j =  1                              :        399908059
  j =  2                              :            45966
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:26.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.37e-3
p-value of test                       :    0.9963

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:17.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:59.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:34.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.35e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:36.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:47.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.77
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.55
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.03
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.82
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.97
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.83
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   97.63
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17451.61
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.59
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.50
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.86
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.99
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.14
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.71
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.41
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.04
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.70
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.13
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.01
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.76
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.25
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.17
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.09
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.72
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.51
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.34
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.47
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.29
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.30
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.52
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  242.34
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.26
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.62
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.46
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.30
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.36
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.22
p-value of test                       :  7.2e-3


-----------------------------------------------
Normal statistic for number of jumps  :   -3.08
p-value of test                       :    0.9990



-----------------------------------------------
CPU time used                    :  00:02:24.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.53
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:25.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 9.50e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 3.60e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.94
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.98
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.88
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.88
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:07.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10118.60
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.6e-3

Kolmogorov-Smirnov- statistic = D-    : 2.79e-3
p-value of test                       :    0.9971

Anderson-Darling statistic = A2       :    5.07
p-value of test                       :  2.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9559.44
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:41.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4801.35
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:47.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4990.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:51.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.12
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.36
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11851.27
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11862.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.41
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000009814

Normal statistic for number of bits   :   0.078
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.04
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999974462

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:34.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 91  HammingWeight2, r = 27          0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 112558108.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5323
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:54.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4484
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:04.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:04.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:55.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:01.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:46.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:14.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:41.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.77
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.99
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.78
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.57
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.98
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:44.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.70
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:00.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7101.29
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.76
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.83
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:02.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.11
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5036.27
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:11.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45612
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869612
  j =  1                              :        399908780
  j =  2                              :            45604
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45817
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869817
  j =  1                              :        399908368
  j =  2                              :            45813
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:26.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:18.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:45.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:59.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:33.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-5
p-value of test                       :    0.9911

Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.019
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.061
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.04
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.92
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.08
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.75
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.29
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.34
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17247.65
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.46
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.66
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.01
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.37
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.34
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.47
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.43
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.14
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.21
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.00
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.36
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.50
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.14
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.09
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.74
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.06
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.45
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.66
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.13
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.12
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.71
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.68
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.65
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.68
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.41
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  318.80
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.09
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.13
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:25.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.71
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:25.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.87

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.47e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 9.17e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.26e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.26
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.72
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.30
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.99
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:07.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 5.83e-3
p-value of test                       :    0.9939

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9772.44
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:43.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.63e-3
p-value of test                       :    0.9973

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5059.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4754.86
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.10
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.01
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11636.57
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11933.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.47
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000007060

Normal statistic for number of bits   :   0.056
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.75
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999987878

Normal statistic for number of bits   :  -0.096
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:49.47

 All tests were passed




Server wird beendet - Lösche Semaphor 113573916.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:52.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:38.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:03.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:04.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:53.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.94
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:14.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:43.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.21
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.15
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.11
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.44
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.95
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.89
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7201.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:41.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.75
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:06.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.66
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.09
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:32.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4933.19
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:12.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46098
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870098
  j =  1                              :        399907805
  j =  2                              :            46096
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45970
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869970
  j =  1                              :        399908062
  j =  2                              :            45966
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:27.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:54.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:34.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 3.97e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.82e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.030
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:40.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.88
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.03
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:48.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.78
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.69
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:43.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.59
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.57
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:29.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.18
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17618.39
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.45
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.12
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.11
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.39
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.53
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.52
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.11
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.65
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.62
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.86
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  428.69
p-value of test                       :    0.9906


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.40
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.22
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.87
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  563.60
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.03
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.55
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.19
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.42
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.53
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.75
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  322.88
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.19
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5214.25
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.22
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.94
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.97
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:24.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.76
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:24.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.55e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.52e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.25e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.49
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.96
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.94
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:06.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:08.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.38
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:50.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4957.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.11
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:49.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.00
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.66
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11932.15
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:30.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.71
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999912311

Normal statistic for number of bits   :   -0.69
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.92
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999900386

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.95
p-value of test                       :    0.03

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:07.42

 All tests were passed




Server wird beendet - Lösche Semaphor 114458652.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:54.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:42.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:42.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:59.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:10.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7163
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:11.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7536
p-value of test                       :  5.7e-3


-----------------------------------------------
CPU time used                    :  00:04:08.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:13.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    2.19
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    2.86
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:15.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:43.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.28
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.12
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.65
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.29
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.30
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.99
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.45
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:08.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7133.87
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:20.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.45
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:47.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.11
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4924.98
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:59.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45732
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869732
  j =  1                              :        399908537
  j =  2                              :            45730
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45749
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869749
  j =  1                              :        399908503
  j =  2                              :            45747
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:32.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:21.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:53.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:12.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 3.41e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.072
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:52.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:53.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.84
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.92
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.98
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.61
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.06
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:50.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.80
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.65
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.35
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.05
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17329.68
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.01
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.41
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.93
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.82
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.87
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.97
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.52
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.25
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.27
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.13
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.99
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.76
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.41
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.62
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.20
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.28
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.18
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.56
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.26
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.55
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.99
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.04
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.86
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.19
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.09
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.61
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4841.99
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.06
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.85
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.74
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:22.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.24
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:23.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   0.043
p-value of test                       :    0.48

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.34e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.22e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.79
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.16
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.73
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:07.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  155.52
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:02:05.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.64e-3
p-value of test                       :    0.9918

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10262.16
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.92
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:04:28.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:57.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4795.01
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:59.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.05
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4263.78
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11523.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11628.33
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:39.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.87
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999924755

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.64
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999826532

Normal statistic for number of bits   :   -1.37
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.040
p-value of test                       :    0.48

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.080
p-value of test                       :    0.47

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:31.40

 All tests were passed




Server wird beendet - Lösche Semaphor 115441692.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:49.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1476
p-value of test                       :  1.5e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334596
  j =  1                              :        599997048
  j =  2                              :             1476
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5279
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:51.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:39.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:05.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:05.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:55.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:01.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.92
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    2.08
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:14.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:44.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.71
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.91
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.33
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.01
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.10
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.05
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.17
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.75
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.11
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:42.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1525.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:02.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7186.52
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.88
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:02.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.29
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.69
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5020.79
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:57.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45918
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869918
  j =  1                              :        399908166
  j =  2                              :            45914
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45466
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869466
  j =  1                              :        399909069
  j =  2                              :            45464
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:27.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:18.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.01e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.13e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:37.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:34.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.13
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:47.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.22
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.90
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.86
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.47
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:39.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.76
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    4.14
p-value of test                       :  7.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.66
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17302.92
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.66
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.17
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.10
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.55
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.71
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.65
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.12
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.26
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.62
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.59
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.48
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.53
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.14
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.64
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.82
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.34
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.89
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.92
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.71
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.89
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.37
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.22
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.10
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5092.16
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  429.78
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.17
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.62
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:22.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.06
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:23.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.59e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.14
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.27
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.17
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:04.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.62
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10123.68
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.57
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.045
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.088
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.057
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:36.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:46.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.97
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4248.25
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11868.65
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.11
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000043399

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.72
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999993218

Normal statistic for number of bits   :  -0.054
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 3.68e-3
p-value of test                       :    0.9962

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.96

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.77

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:00:46.55

 All tests were passed




Server wird beendet - Lösche Semaphor 116719644.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:50.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1464
p-value of test                       :  3.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334584
  j =  1                              :        599997072
  j =  2                              :             1464
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5363
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:51.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:39.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:38.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:04.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:55.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:01.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.91
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    2.03
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:15.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.52
p-value of test                       :  5.4e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.21
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.87
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.59
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.74
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.19
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.91
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  291.70
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.22
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1497.91
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7080.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:02.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.17
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.89
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:32.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5118.11
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:02.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45741
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869741
  j =  1                              :        399908518
  j =  2                              :            45741
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45787
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869787
  j =  1                              :        399908426
  j =  2                              :            45787
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:28.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:16.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.35e-3
p-value of test                       :    0.9928

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9910


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:34.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.71e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:36.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.76
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:48.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.00
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.22
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.42
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.13
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.46
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.76
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.75
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.68
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17443.79
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.75
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.83
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.06
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.17
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.34
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.94
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.72
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.83
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.69
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.40
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.68
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.11
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.20
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.53
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.45
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.65
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.42
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.50
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.72
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.76
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.90
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.66
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.36
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.65
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.89
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.28
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.51
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.94
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -1.23
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:23.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.54
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    1.49
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:23.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.05

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.93

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.75e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.54e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.49
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.36
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.23
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:04.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.21
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10207.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9878.49
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.54
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.062
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:40.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:51.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3954.21
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.07
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11498.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11758.69
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.41
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999947036

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.46
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999948479

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.88
p-value of test                       :    0.97

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.87
p-value of test                       :    0.97

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:24.18

 All tests were passed




Server wird beendet - Lösche Semaphor 117735452.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1270
p-value of test                       :    0.9948

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334390
  j =  1                              :        599997460
  j =  2                              :             1270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1488
p-value of test                       :  5.0e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334608
  j =  1                              :        599997024
  j =  2                              :             1488
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:50.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:39.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7108
p-value of test                       :    0.9931


-----------------------------------------------
CPU time used                    :  00:02:38.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:05.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:05.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:56.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:02.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9960


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.28
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.95
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:14.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:43.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.59
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.79
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.58
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.69
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.57
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:44.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.10
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7026.97
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:40.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.86
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:02.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.59
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.19
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:35.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5088.06
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:10.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45673
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869673
  j =  1                              :        399908660
  j =  2                              :            45661
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45939
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869939
  j =  1                              :        399908124
  j =  2                              :            45935
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:26.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:16.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:45.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:34.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 5.96e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:35.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.00
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.69
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.23
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.07
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.09
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.06
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17556.80
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.42
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   61.65
p-value of test                       :  3.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.01
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.76
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.20
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.66
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.75
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.41
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.52
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.51
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  407.22
p-value of test                       :    0.9991    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.45
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.82
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.78
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  430.52
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  103.81
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.58
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.28
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  306.98
p-value of test                       :    0.9985


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.02
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.32
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.40
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.72
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  445.30
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.61
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.37
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.75
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.39
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:22.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.39
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:21.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.02e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 4.10e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.19
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.29
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:05.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.22
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:07.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9856.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:39.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.24
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
p-value of test                       :    0.9929

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.1e-3

Anderson-Darling statistic = A2       :    5.03
p-value of test                       :  2.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5188.98
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:01:51.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.13
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4006.93
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11831.57
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11670.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.48
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999914042

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.49
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999830993

Normal statistic for number of bits   :   -1.34
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.84
p-value of test                       :    0.03

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:09.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           5.0e-4
 76  RandomWalk1 J (L=1000, r=0)     0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 118685724.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5368
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:51.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:04.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:04.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:55.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:00.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    4.49
p-value of test                       :  5.0e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     985
p-value of test                       :  2.7e-3

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    2.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    2.00
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:13.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    2.09
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    2.37
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    3.99
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:02:42.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.23
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.25
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.14
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.58
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.41
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.59
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7104.19
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:42.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.58
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:03.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.34
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.26
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4997.17
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:54.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45871
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869871
  j =  1                              :        399908260
  j =  2                              :            45867
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45713
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869713
  j =  1                              :        399908577
  j =  2                              :            45707
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:27.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:15.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:02.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:55.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:32.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.21e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 5.96e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:35.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:34.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.33
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.43
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.08
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.28
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.72
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.07
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.83
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.82
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.13
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17063.33
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.55
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.73
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.63
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.04
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.13
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.46
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.38
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.50
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.65
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.47
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.60
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.47
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.56
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.62
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.20
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.78
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.21
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.47
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.83
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.30
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.95
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.71
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.11
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5081.05
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.53
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.31
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.78
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:22.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.40
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:24.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    2.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.29e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 7.96e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.59
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.37
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.02
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:04.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.46
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:05.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.03
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.23
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:42.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5054.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.47
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4232.17
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.26
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11754.27
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.41
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.71
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000105427

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.81
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999895736

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         : -6.62e-3
p-value of test                       :    0.50

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:20.20

 All tests were passed




Server wird beendet - Lösche Semaphor 119668764.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1468
p-value of test                       :  2.8e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334588
  j =  1                              :        599997064
  j =  2                              :             1468
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5519
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:56.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:43.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:00.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:12.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:11.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:04:10.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:14.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9955

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.63
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    2.06
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:14.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:42.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.64
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.92
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.38
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.73
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.36
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.74
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:58.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.26
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:09.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6923.86
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:57.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.84
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.73
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:11.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.54
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.32
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:41.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4976.26
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:59.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46027
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870027
  j =  1                              :        399907948
  j =  2                              :            46023
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45802
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869802
  j =  1                              :        399908400
  j =  2                              :            45794
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9947

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:31.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:23.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:11.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:57.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.00e-3
p-value of test                       :    0.9957

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:38.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.01e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.32e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 9.59e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.092
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.15
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.13
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.05
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.21
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.50
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.50
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.03
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.03
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17518.92
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.56
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.31
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.69
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.13
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.41
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.29
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.15
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.20
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.44
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.61
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.44
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  424.20
p-value of test                       :    0.9939


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.27
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.32
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.06
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.43
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.90
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.77
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.28
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.42
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.36
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4853.93
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.99
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  157.16
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.28
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.95
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5117.77
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.13
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.98
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.62
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -1.60
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:22.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.48
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 4.01e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 4.38e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.18
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.24
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.38
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:08.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10198.99
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9702.64
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:12.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:04:36.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.01
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:53.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4814.25
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.01
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.71
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11767.30
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:33.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:37.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.51
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000044710

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.63
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000091984

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:36.69

 All tests were passed




Server wird beendet - Lösche Semaphor 120553500.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5317
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:54.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4199
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7167
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:41.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:05.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:05.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:55.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7472
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:01.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    2.40
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.07
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.86
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:14.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    3.35
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:44.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.72
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.10
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.04
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.97
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.31
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1368.45
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7109.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:41.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.70
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:03.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.21
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.62
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.06
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:13.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45697
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869697
  j =  1                              :        399908611
  j =  2                              :            45687
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45758
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869758
  j =  1                              :        399908487
  j =  2                              :            45752
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9976


-----------------------------------------------
CPU time used                    :  00:02:27.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:19.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:01.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:33.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 9.80e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.53e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.072
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:33.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.42
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.54
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.50
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.24
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:48.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.38
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   50.53
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:01:43.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.22
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.35
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17332.36
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.50
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.42
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.69
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.38
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.56
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.42
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.95
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.54
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.55
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.38
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.66
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.90
p-value of test                       :    0.9948


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.50
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.19
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.88
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.52
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.74
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.20
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.30
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.28
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.48
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.55
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4774.24
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.43
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.19
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.74
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4869.65
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  466.32
p-value of test                       :  1.3e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  241.19
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:32.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.30
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    1.91
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:14.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.20
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   0.016
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:13.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    2.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.79e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 6.63e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 3.38e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.88
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.60
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.90
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9982.74
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:24.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3982.59
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11482.58
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11616.10
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.68
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000106072

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.11
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999916574

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  2.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.17
p-value of test                       :    0.99

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.24
p-value of test                       :    0.01

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:57:30.70

 All tests were passed




Server wird beendet - Lösche Semaphor 121765916.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5464
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:45.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:38.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:38.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:58.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:08.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:08.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:08.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:10.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    2.33
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    4.02
p-value of test                       :  8.5e-3

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:43.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:13.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.37
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:47.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.91
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.31
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.21
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.59
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.85
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.69
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.08
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.31
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1507.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:09.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6920.73
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:58.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.29
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.16e-3
p-value of test                       :    0.9957

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   87.21
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:15.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.57
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.44
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:57.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45755
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869755
  j =  1                              :        399908491
  j =  2                              :            45753
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46324
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870324
  j =  1                              :        399907354
  j =  2                              :            46320
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:27.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:19.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:53.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:37.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.96e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 2.80e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:24.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:24.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.10
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.74
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.81
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.77
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:54.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.07
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:30.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  160.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17423.48
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.28
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.37
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.67
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.46
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.81
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.09
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.25
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.41
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.61
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.36
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.87
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.34
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.99
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.83
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.92
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.99
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.16
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.60
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.32
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.46
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.41
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.91
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4807.98
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.90
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.71
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.14
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.97
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.87
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.37
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.96
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.73
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :  -0.028
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:25.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.76
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:25.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.38e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 6.59e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.25
p-value of test                       :    0.9961

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:33.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.06
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:38.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.18
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:27.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.12
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:28.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9829.84
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9908.17
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:11.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:04:39.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.07
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:53.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.09
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4287.57
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11749.81
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12207.97
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.00
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000183247

Normal statistic for number of bits   :    1.45
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.65
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999896432

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:14.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         : -8.08e-3
p-value of test                       :    0.50

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:20:18.13

 All tests were passed




Server wird beendet - Lösche Semaphor 102531101.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5451
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:49.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:39.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:38.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:55.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:03.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:08.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:58.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:01.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.90
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    3.64
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    2.84
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:13.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.36
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:43.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.58
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.85
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.86
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.96
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.19
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.02
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:46.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.93
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:02.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7046.51
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9948

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.57
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.56e-3
p-value of test                       :    0.9974

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   97.79
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:03:03.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.01
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.96
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5191.17
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:52.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45494
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869494
  j =  1                              :        399909014
  j =  2                              :            45490
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45753
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869753
  j =  1                              :        399908505
  j =  2                              :            45731
  j =  3                              :               11
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:27.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:17.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:44.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:00.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:54.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.95e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 9.97e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.01e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.28e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.091
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:43.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.23
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.94
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.89
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.66
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.47
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.00
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.17
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.22
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.013
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.18
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17178.02
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.01
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.46
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.83
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.34
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.07
p-value of test                       :    0.9927


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.41
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.38
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.91
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.35
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.46
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.08
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.93
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.32
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.27
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.67
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.96
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.59
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.53
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.65
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.91
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.74
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.38
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.79
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.81
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.77
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.06
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.60
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.19
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.94
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.82
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.49
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -1.21
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:24.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.21
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:24.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.85
p-value of test                       :    0.03

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.96e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.70
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.16
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.21
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:06.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.96
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:07.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.28e-3
p-value of test                       :    0.9945

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9625.32
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.56
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:04:01.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.84
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:48.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.93
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.99
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3968.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11853.41
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.72
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000121834

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.89
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000038908

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :  -0.066
p-value of test                       :    0.53

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:42.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 69  MatrixRank, L=1000, r=26        0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 103579677.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:49.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:39.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4231
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:12.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:08.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7611
p-value of test                       :  3.4e-4    *****


-----------------------------------------------
CPU time used                    :  00:04:13.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    2.03
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:14.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:40.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.85
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.37
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.02
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.41
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.55
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  391.05
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1526.94
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7017.30
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.39
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.53
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:18.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.19
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.54
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:39.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5200.27
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:54.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45667
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869667
  j =  1                              :        399908671
  j =  2                              :            45657
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45866
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869866
  j =  1                              :        399908272
  j =  2                              :            45858
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:29.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:14.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  6.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:01.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.87e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.66e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:24.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:55.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:52.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.61
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.68
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.26
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.46
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.89
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.68
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:51.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.09
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.90
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.50
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:30.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.47
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.29
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17182.26
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.14
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.16
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    9.15
p-value of test                       :    0.9984


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.43
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.09
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.89
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.09
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.45
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.45
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.53
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.47
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.58
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.77
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.41
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.91
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.39
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.60
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.49
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.82
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.02
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.13
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4888.42
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.03
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.87
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.60
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.93
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.94
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.48
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.78
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.55
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:23.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.73
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -1.28
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:23.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.60e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.47
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.29
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.59
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:08.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.34
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:06.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.71
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.30
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.044
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:04:21.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.57
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.92
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.36
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.98
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11770.84
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.05
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000008785

Normal statistic for number of bits   :   0.069
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.99
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000116752

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:10.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 21  BirthdaySpacings, t = 16        3.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 104529949.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:49.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5518
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:55.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7125
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:05.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:05.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7475
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:57.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:02.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9936

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.31
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.88
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     340
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:12.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.08
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:42.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.88
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.01
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.53
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.51
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.34
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.45
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:03.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7090.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.40
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:01.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.73
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.14
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:35.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5003.28
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:57.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45878
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869878
  j =  1                              :        399908248
  j =  2                              :            45870
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45834
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869834
  j =  1                              :        399908336
  j =  2                              :            45826
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:27.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:18.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:55.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:35.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.82e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.74e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 2.71e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.45
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:01:37.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.44
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.38
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.36
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.44
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.32
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.43
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.24
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.02
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17260.81
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.15
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.30
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.27
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.58
p-value of test                       :  9.5e-3


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.04
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.25
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.96
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.58
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.43
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.24
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.74
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.96
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.46
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.78
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.36
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.52
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4812.67
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.29
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.85
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.59
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.27
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.80
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.71
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:34.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.65
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:24.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.46
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:26.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.84e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 8.82e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.40
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.57
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.73
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:05.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.47
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:05.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10043.98
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.23
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:42.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.24
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.18
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:49.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4240.70
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.28
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.46
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.03
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999964331

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.46
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000099826

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.037
p-value of test                       :    0.49

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :  -0.086
p-value of test                       :    0.53

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:20.07

 All tests were passed




Server wird beendet - Lösche Semaphor 105545757.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:51.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:53.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4207
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:05.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:55.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7163
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:01.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    2.32
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:13.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    2.15
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.95
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.29
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.68
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.10
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.68
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.70
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.57
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:42.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:03.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7016.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.83
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.78
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:00.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.08
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.60
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4929.60
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:55.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45873
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869873
  j =  1                              :        399908257
  j =  2                              :            45867
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45828
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869828
  j =  1                              :        399908347
  j =  2                              :            45822
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:24.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:16.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:54.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 3.17e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.087
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:44.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.38
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.65
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.00
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.74
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.47
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.84
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.34
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17326.27
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.09
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.37
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.08
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.70
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.38
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.66
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.00
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.61
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.94
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.51
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.23
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.90
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.31
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.34
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.82
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.20
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.46
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.15
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4756.87
p-value of test                       :    0.9932


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.22
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.14
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.47
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.81
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5192.25
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.65
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.00
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.64
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   -1.00
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:22.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.27
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:24.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.93e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.53e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 6.21e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.82
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.11
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.02
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:05.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.68
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9810.66
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9836.57
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:45.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.45
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:47.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4264.35
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12038.18
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11772.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.11
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000067144

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.63
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999965063

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:31.70

 All tests were passed




Server wird beendet - Lösche Semaphor 106561565.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5445
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:54.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:39.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:57.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:04.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:05.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.94
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     638
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:13.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:36.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.09
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.74
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.51
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.38
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.99
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.75
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.20
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.63
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:02.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7066.73
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.63
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.03
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.70
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5153.92
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:56.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45940
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869940
  j =  1                              :        399908120
  j =  2                              :            45940
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46171
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870171
  j =  1                              :        399907660
  j =  2                              :            46167
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:27.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:46.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:01.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  3.1e-3

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:54.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.048
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:43.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.61
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.80
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.49
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.02
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.58
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:43.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.97
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.10
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17582.48
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.11
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.62
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.24
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.73
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.12
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.95
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.71
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.76
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.06
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.57
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.44
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.23
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.72
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.64
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.62
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.56
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.29
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.96
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.70
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.90
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5085.03
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.92
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.72
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.08
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.25
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4858.78
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.41
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.08
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:24.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.39
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:23.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.23

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.86
p-value of test                       :    0.03

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.74e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 9.52e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.00e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.51
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.30
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.72
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:04.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.18
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:07.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9978

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9967.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.088
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:50.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.43
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.40
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.75
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.07
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11980.75
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.10
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999997850

Normal statistic for number of bits   :  -0.017
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.72
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999931868

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.26
p-value of test                       :    0.01

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:31.63

 All tests were passed




Server wird beendet - Lösche Semaphor 107511837.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9974


-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5367
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:52.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:39.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:04.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:55.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:01.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.13
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    2.80
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     829
p-value of test                       :    0.9913

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    3.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.14
p-value of test                       :    0.9990    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.72
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:13.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    5.68
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:02:43.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.39
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.87
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.06
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.89
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7159.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:03.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.57
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.74
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:33.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4981.69
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:03.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45606
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869606
  j =  1                              :        399908791
  j =  2                              :            45600
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45716
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869716
  j =  1                              :        399908568
  j =  2                              :            45716
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:27.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:18.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:46.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:33.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.42e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:38.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.062
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.10
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.53
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.80
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.67
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.04
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.96
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.01
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17170.16
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.59
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.32
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.17
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.96
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.99
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.13
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.15
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.95
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.07
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.61
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.46
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  444.16
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.33
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.55
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.16
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.90
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  176.19
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.86
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.21
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.77
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.32
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  141.09
p-value of test                       :    0.9994    *****


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.21
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.49
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.51
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.17
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.52
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.17
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:24.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.92
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.90e-4
p-value of test                       :    0.9990    *****

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.79
p-value of test                       :  3.8e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.16
p-value of test                       :  8.0e-4    *****

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 6.90e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.89e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.26
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.36
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.49
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:06.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.31
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:05.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9933.72
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.39
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:50.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.68
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.5e-3

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5040.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4295.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3926.80
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12075.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11790.31
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.26
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000074287

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.08
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000091915

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:37.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP1, t = 5          0.9990 
 78  RandomWalk1 C (L=10000, r=0)    0.9994 
 82  LempelZiv, r = 0                8.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 108462109.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9907


-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5504
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:52.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4446
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7170
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:38.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:03.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:05.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:56.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:04:02.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    2.30
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    2.66
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:13.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.39
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.73
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.69
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.08
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.46
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.90
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.20
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.38
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:43.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.92
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6833.01
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.13
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:02.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.62
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.17
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4893.28
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9968


-----------------------------------------------
CPU time used                    :  00:03:04.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45667
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869667
  j =  1                              :        399908671
  j =  2                              :            45657
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45750
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869750
  j =  1                              :        399908503
  j =  2                              :            45744
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:27.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9952


-----------------------------------------------
CPU time used                    :  00:02:17.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:44.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:01.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.6e-3

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:32.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.48e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.04e-5
p-value of test                       :    0.9957

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.52
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.84
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.03
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.39
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:42.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.20
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.01
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.95
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17236.24
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.64
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.43
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.16
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.89
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.44
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.56
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.89
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.22
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.17
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.68
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.48
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.57
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.94
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.80
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  573.10
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.73
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.42
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.64
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.19
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5053.45
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.04
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.76
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.05
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.50
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4913.47
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.23
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.39
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.35
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:24.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.10
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -1.52
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:24.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 3.52e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.01e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.14
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   22.55
p-value of test                       :  4.0e-3

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:05.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.41
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:07.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.88
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9812.87
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : -6.86e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:46.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5020.91
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.53
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:50.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.74
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.54
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.82
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11558.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.06
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999923264

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   84.04
p-value of test                       :  5.5e-3


-----------------------------------------------
Total number of bits:  8000041746

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   0.029
p-value of test                       :    0.49

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:45.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 51  SampleProd, t = 16              0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 109412381.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5334
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:56.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:00.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4210
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:03.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:51.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:52.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:29.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:05:31.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.83
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:12.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:33.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.28
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.05
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  275.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  474.52
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:35.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1349.14
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:47.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7225.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:41.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.89
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:17.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.88
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.46
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.52
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:55.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45898
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869898
  j =  1                              :        399908207
  j =  2                              :            45892
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45783
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869783
  j =  1                              :        399908436
  j =  2                              :            45779
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:35.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:25.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  4.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:12.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.46e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.74
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:01:50.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.08
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.10
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.01
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.96
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:40.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.37
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.41
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:51.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.95
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  163.20
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 2.56e-3
p-value of test                       :    0.9974

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17908.06
p-value of test                       :  5.5e-3



-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.12
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.17
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.04
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.56
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.01
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.05
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.19
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.16
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.43
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.72
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.83
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.06
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.07
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.67
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.81
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.34
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.83
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.48
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.73
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.37
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.08
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.26
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5190.87
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.06
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.49
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.61
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.77
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.75
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.94
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.12
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:24.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.92
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:24.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.61e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 7.46e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.32e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.24
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.91
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.96
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.34
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:08.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.07
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10165.12
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.071
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.037
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:04:23.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.97
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:57.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.65
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4001.17
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.38
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.19
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.14
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:35.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.40
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999932435

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.97
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999949067

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:19:12.20

 All tests were passed




Server wird beendet - Lösche Semaphor 110362653.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:54.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:04.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:56.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:01.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    2.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    3.67
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:15.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    2.42
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:42.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.04
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.60
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.40
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.51
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.63
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.65
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.47
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1355.61
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:01.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7135.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.33
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:04.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.89
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.50
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5016.23
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:04.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45743
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869743
  j =  1                              :        399908515
  j =  2                              :            45741
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45675
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869675
  j =  1                              :        399908656
  j =  2                              :            45663
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:28.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  9.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:18.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 2.92e-3
p-value of test                       :    0.9969

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  8.8e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:59.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.71e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.04e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.02e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:35.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.37
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.44
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.79
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.82
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.00
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.20
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17550.85
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.71
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.38
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.40
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.58
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.40
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.77
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.22
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.39
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.15
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.15
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.88
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.12
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.16
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   46.85
p-value of test                       :    0.9943


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.24
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.74
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.22
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.30
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.55
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.79
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.01
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5160.83
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.70
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.33
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.75
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.31
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4888.92
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.26
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.66
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.48
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -2.07
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:22.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.05
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:26.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.098
p-value of test                       :    0.54

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.36e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 9.57e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.66e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 6.97e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.29
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.72
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.34
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:07.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.71
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:06.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9853.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9740.04
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.045
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:42.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.44
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4305.70
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4270.34
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11955.32
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11786.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.29
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000105772

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.70
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999813710

Normal statistic for number of bits   :   -1.47
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:05.27

 All tests were passed




Server wird beendet - Lösche Semaphor 111509533.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5387
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:52.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7102
p-value of test                       :    0.9944


-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:04.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:55.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7498
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.01
p-value of test                       :  8.8e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.95
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    2.40
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     534
p-value of test                       :    0.9967

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:14.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.10
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    6.76
p-value of test                       :  4.4e-4    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     187
p-value of test                       :  2.0e-3

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.72
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.52
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.10
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.65
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.58
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.95
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.05
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.88
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:01.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7177.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.35
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:04.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.62
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   88.91
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5022.07
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:54.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45937
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869937
  j =  1                              :        399908129
  j =  2                              :            45931
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45876
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869876
  j =  1                              :        399908253
  j =  2                              :            45866
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:26.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:55.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:34.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.014
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.040
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:35.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.63
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.54
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.12
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.17
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   22.95
p-value of test                       :  4.1e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.77
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17342.84
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.61
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.12
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.03
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.85
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.10
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.25
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.26
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.74
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.58
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.19
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.53
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.92
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.76
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.26
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.16
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.93
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.09
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.09
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.11
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.33
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  292.13
p-value of test                       :    0.9998    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.61
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.41
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:34.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.92
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.78
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5114.02
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.78
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:34.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.08
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :   -2.18
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:19.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.02
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:22.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:47.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.45e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.30
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.12
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:07.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:06.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9898.90
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9896.01
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:41.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5005.86
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.93
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.67
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.04
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.37
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.48
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999882836

Normal statistic for number of bits   :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.20
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  7999926060

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :  -0.037
p-value of test                       :    0.51

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:44.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP1, t = 16         4.4e-4
 69  MatrixRank, L=1000, r=26        4.1e-5
 78  RandomWalk1 M (L=10000, r=0)    0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 112492573.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:52.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:40.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:04.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:55.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7474
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:00.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:13.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9916


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:42.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.60
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.95
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.60
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.57
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.80
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1531.13
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6929.13
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.64
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.42
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:04.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.16
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.72
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:33.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5168.12
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:59.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45409
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869409
  j =  1                              :        399909189
  j =  2                              :            45395
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46194
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870194
  j =  1                              :        399907615
  j =  2                              :            46188
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:28.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:20.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:46.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.90e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 9.97e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:33.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.42
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.03
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.42
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:38.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.20
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.62
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.89
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17698.64
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.74
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.38
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.84
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.73
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.86
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.43
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.97
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   50.37
p-value of test                       :  1.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.13
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.69
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.77
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.26
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.58
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.77
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.73
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.26
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.83
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.43
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.76
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.03
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5128.06
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.83
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.20
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.81
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.67
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4854.66
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.68
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.50
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.64
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -1.06
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:24.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.74
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:24.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.83
p-value of test                       :    0.97

Sample variance                       :    2.43
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.63e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.86e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.15
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.93
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.88
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.26
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:05.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9784.03
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9836.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:45.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.20
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9913

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.33
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.15
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12055.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.72
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.24
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000171451

Normal statistic for number of bits   :    1.36
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.58
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999933635

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.095
p-value of test                       :    0.46

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:54.18

 All tests were passed




Server wird beendet - Lösche Semaphor 113377309.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:48.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5441
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:53.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4447
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:59.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:09.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:09.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:54.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:59.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    2.55
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     841
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:13.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.93
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.80
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.69
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.41
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.05
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.71
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:54.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.04
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7077.51
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:09.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.82
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.36
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:01.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.87
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.45
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4919.77
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:55.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45815
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869815
  j =  1                              :        399908372
  j =  2                              :            45811
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45881
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869881
  j =  1                              :        399908241
  j =  2                              :            45875
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:28.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 2.58e-3
p-value of test                       :    0.9972

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9991    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 9.79e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:33.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:35.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.65
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.75
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.68
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:48.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.54
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.01
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.49
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:38.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.21
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.75
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17362.15
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.20
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.63
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.24
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.19
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.90
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.60
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.85
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.55
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.48
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.23
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.15
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.56
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.17
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.21
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.56
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.73
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.50
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.33
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.30
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.23
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.59
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.01
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  323.21
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  314.24
p-value of test                       :    0.9961


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.87
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.92
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.42
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.93
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    2.08
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:23.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.51
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    2.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.00e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.90
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.83
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.12
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:14.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.24
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:13.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.22
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10015.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.088
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:41.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5030.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3991.76
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11799.60
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11615.85
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.36
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999820547

Normal statistic for number of bits   :   -1.42
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   31.37
p-value of test                       :    0.9942


-----------------------------------------------
Total number of bits:  7999995519

Normal statistic for number of bits   :  -0.035
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.21
p-value of test                       :    0.01

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:40.95

 All tests were passed




Server wird beendet - Lösche Semaphor 114360349.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5355
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:53.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:39.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:03.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:03.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:56.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:00.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     952
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    2.92
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    2.36
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     339
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:12.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:41.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.04
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.78
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.76
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.07
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.10
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.72
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.26
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:02.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7007.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.57
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.62
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.98
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:10.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   19.70
p-value of test                       :  1.4e-3


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.43
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:32.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5038.10
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:54.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46240
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870240
  j =  1                              :        399907524
  j =  2                              :            46232
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46321
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870321
  j =  1                              :        399907361
  j =  2                              :            46315
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:27.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:19.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:45.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.04e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.066
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:32.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:34.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:48.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.34
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.57
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.38
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.57
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.59
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.72
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17221.45
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.84
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.36
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.28
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.51
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.13
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.23
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.08
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.60
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.31
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.46
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.43
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.21
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.57
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.49
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.36
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.54
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.03
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.57
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.48
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.57
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.08
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.60
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.07
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.13
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.72
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.65
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5086.88
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.81
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.68
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.14
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:25.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.69
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.84e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 5.03e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.29
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.18
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.98
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:08.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.76
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:05.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10150.04
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.59
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:42.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4990.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.95
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:50.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.96
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11758.71
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11672.36
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.08
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000004675

Normal statistic for number of bits   :   0.037
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.75
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999886964

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    2.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   0.017
p-value of test                       :    0.49

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:49.68

 All tests were passed




Server wird beendet - Lösche Semaphor 115343389.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5461
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:53.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:04.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:04.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:54.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:59.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:13.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.94
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:42.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.95
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.86
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.86
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  474.47
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:43.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1381.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7046.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.15
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:03.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.48
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:32.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5188.00
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:58.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45539
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869539
  j =  1                              :        399908924
  j =  2                              :            45535
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46119
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870119
  j =  1                              :        399907763
  j =  2                              :            46117
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:27.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:44.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:00.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:33.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.95e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 1.46e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:34.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.08
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.68
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:39.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.59
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.21
p-value of test                       :  7.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.72
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.80
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17343.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.78
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.98
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.52
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.00
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.11
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.90
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.80
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.36
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.01
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.40
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.81
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.43
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.17
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.35
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.07
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.99
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.46
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.14
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.52
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.20
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.70
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.03
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.93
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.53
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.38
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.96
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4931.36
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.78
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.03
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.20
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:25.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.75
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:25.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.83e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.07
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.45
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:05.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.02
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:05.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9787.24
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10117.07
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.065
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:45.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.04
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.27
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:50.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.14
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4224.28
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.59
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.89
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.61
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000062722

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.95
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000144316

Normal statistic for number of bits   :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.18
p-value of test                       :    0.01

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    2.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:07.00

 All tests were passed




Server wird beendet - Lösche Semaphor 116359197.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:53.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7148
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:10.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:03.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:04.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:14.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.12
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.16
p-value of test                       :    0.9974

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:44.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.86
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.21
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   83.19
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.44
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.89
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:10.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7106.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.61
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.78
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:18.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.62
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:46.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.00
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4850.23
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:54.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46029
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870029
  j =  1                              :        399907947
  j =  2                              :            46019
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45615
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869615
  j =  1                              :        399908772
  j =  2                              :            45611
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:32.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9907


-----------------------------------------------
CPU time used                    :  00:02:21.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:52.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:10.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:37.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.48e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:43.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.66
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:01:43.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.33
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.99
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.95
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.40
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.12
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.43
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:52.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9968

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.31
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.61
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.15
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17622.89
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.74
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.22
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.55
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.04
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.68
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.18
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.77
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.47
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.80
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.44
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.79
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  177.35
p-value of test                       :  9.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.22
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.19
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.26
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.50
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.24
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.23
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.56
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.80
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5111.66
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.74
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.66
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.06
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.06
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.69
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.95
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.17
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.25
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:24.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.13
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:24.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    2.72
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 7.80e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.34
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.72
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.99
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:05.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10088.38
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10099.58
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:04:26.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.53
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5046.74
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:59.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.59
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11664.15
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:34.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.86
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.85
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999989525

Normal statistic for number of bits   :  -0.083
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.06
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999970880

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:29.68

 All tests were passed




Server wird beendet - Lösche Semaphor 117276701.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:54.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:06.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7478
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:07.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:05.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:09.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:13.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    2.20
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    3.67
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:45.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.45
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.58
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.43
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.52
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.70
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:31.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.89
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:56.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.00
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7163.81
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:17.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.67
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.83
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:39.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5038.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:58.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46017
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870017
  j =  1                              :        399907969
  j =  2                              :            46011
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46021
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870021
  j =  1                              :        399907963
  j =  2                              :            46011
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:31.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:18.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:57.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:39.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.64e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -5.73e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:51.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.30
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.53
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   50.98
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:01:51.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.3e-3

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.9998    *****

Anderson-Darling statistic = A2       :    4.13
p-value of test                       :  7.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.48
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.52
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17397.96
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.43
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.62
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.10
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.99
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.42
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.85
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.99
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.25
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.45
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.52
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.30
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.00
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.43
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.91
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.96
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.30
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.61
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.25
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.03
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.33
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.29
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.85
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.87
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.45
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.49
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.52
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.94
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  431.64
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.30
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:34.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.71
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:22.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.03
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:23.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 4.65e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.16e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 7.64e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.49
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   21.21
p-value of test                       :  6.6e-3

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:04.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.82
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10219.48
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10117.23
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:04:25.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.90
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4778.80
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.08
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4246.86
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12218.59
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:01:35.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11934.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.77
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999899429

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.74
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000013159

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   0.012
p-value of test                       :    0.50

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:53.26

 All tests were passed




Server wird beendet - Lösche Semaphor 118554653.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:52.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:08.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:09.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:06.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:07.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     849
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:14.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.43
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:44.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.37
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.00
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.73
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.99
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:50.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.41
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:04.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7238.32
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.90
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:15.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.70
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.29
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:51.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4966.20
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:08.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46061
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870061
  j =  1                              :        399907884
  j =  2                              :            46049
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45479
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869479
  j =  1                              :        399909045
  j =  2                              :            45473
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:16.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:31.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:18.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:05.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :  3.6e-4    *****

Anderson-Darling statistic = A2       :    4.28
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:01:57.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.42e-3
p-value of test                       :    0.9963

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:38.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.99e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:51.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.87
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.57
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.45
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.75
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:49.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.09
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.04
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.35
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17576.01
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.59
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.06
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.95
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.43
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.24
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.65
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.26
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.47
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.65
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.01
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.02
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.17
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.87
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.50
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.50
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.16
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.40
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.74
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.84
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.21
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.48
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.20
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5153.43
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.19
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.83
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.84
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.64
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.63
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.22
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.60
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.73
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    1.48
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:23.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.11
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:22.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         : -5.43e-3
p-value of test                       :    0.50

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 4.00e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.33e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 7.60e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.51
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.62
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.12
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:04.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.72
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:04.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.26
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10071.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:18.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.32
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:54.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:57.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.67
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4245.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11650.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.06
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999984863

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.67
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000007798

Normal statistic for number of bits   :   0.062
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:12.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:54.69

 All tests were passed




Server wird beendet - Lösche Semaphor 119701533.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5384
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:52.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:58.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:06.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:06.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7177
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:56.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:02.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.90
p-value of test                       :  9.9e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.15
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    2.30
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    4.04
p-value of test                       :  8.3e-3

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     642
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:13.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.18
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:42.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.71
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.23
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.04
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.94
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.80
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.01
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:43.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.20
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:02.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7152.16
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:41.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   86.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:01.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.54
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.86
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:34.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4952.36
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:10.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46235
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870235
  j =  1                              :        399907530
  j =  2                              :            46235
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46074
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870074
  j =  1                              :        399907853
  j =  2                              :            46072
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  1.9e-3

Kolmogorov-Smirnov- statistic = D-    : 3.18e-3
p-value of test                       :    0.9964

Anderson-Darling statistic = A2       :    3.85
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9968


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:27.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  6.5e-3

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:20.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:03.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:56.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:34.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.12
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.62
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.38
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.49
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.53
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.45
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17671.38
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.49
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.61
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.07
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.97
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.56
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.49
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.46
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.77
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.58
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.98
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.55
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.31
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.64
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.84
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.15
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.67
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.29
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.85
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.26
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.08
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.34
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.85
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.86
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.18
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.04
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  452.32
p-value of test                       :  9.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.06
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.01
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.97
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   33.84
p-value of test                       :  7.1e-4    *****


-----------------------------------------------
Normal statistic for number of jumps  :    2.29
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:02:24.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.74
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:22.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    2.49
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.82
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.55
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.59
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.73
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:05.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :  4.8e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    6.10
p-value of test                       :  9.5e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9547.04
p-value of test                       :    0.9994    *****

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10147.19
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:35.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4997.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:51.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.66
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.71
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11728.54
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11776.69
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.14
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000043633

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   28.36
p-value of test                       :    0.9984


-----------------------------------------------
Total number of bits:  8000099685

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 7.17e-3
p-value of test                       :    0.9924

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.73
p-value of test                       :    0.96

Sample variance                       :    1.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:25.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0               7.1e-4
 90  HammingWeight2, r = 0           0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 120750109.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:53.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:42.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:01.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:11.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:05.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:05.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.16
p-value of test                       :    0.9977

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.61
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:15.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:45.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.01
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.95
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.69
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.04
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.16
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.92
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.97
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:05.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7153.23
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:55.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:13.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.06
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.26
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4872.30
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:05.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45981
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869981
  j =  1                              :        399908040
  j =  2                              :            45977
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45820
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869820
  j =  1                              :        399908361
  j =  2                              :            45818
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:31.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:18.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:52.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:04.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  5.9e-3

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:56.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:24.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:44.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.39
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.41
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.47
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.20
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.38
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.43
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.90
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.26
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.12
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:11.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :  8.4e-4    *****

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17826.26
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.23
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.49
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.26
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.54
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.85
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.52
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.29
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.14
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.56
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.34
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.96
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.09
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.53
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.17
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.52
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.11
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.83
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.21
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.71
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.77
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.80
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.86
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.95
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:33.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.22
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.72
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5138.96
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.46
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.61
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.62
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:12.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.29
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:12.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.46e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 8.21e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.59e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.02
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.49
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.38
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.89
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:54.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.82
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10218.00
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.94
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:20.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.59
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:45.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:45.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.74
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.30
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11641.38
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11961.15
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.74
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999965216

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.75
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999962039

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:56.62

 All tests were passed




Server wird beendet - Lösche Semaphor 121733149.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1475
p-value of test                       :  1.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334595
  j =  1                              :        599997050
  j =  2                              :             1475
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5484
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:41.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:34.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:53.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:01.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:01.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:54.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:59.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.92
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:08.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:35.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.58
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.98
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.15
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.94
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.42
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.57
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.48
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:45.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.22
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6942.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.95
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:02.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.60
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.14
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5151.80
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:58.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45941
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869941
  j =  1                              :        399908121
  j =  2                              :            45935
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45857
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869857
  j =  1                              :        399908287
  j =  2                              :            45855
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:27.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:17.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:51.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.16e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:37.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:48.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.13
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.60
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.82
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:39.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.62
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.66
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.69
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:31.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.68e-3
p-value of test                       :    0.9906

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.2e-3

Anderson-Darling statistic = A2       :    4.04
p-value of test                       :  8.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  175.89
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17331.92
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:55.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.83
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.38
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.29
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.31
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.26
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.81
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.23
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.92
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.18
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.65
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.07
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.78
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.25
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.05
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.18
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:47.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.05
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.91
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.29
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.27
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.25
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:47.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.53
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.68
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.86
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.06
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.60
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.95
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5136.10
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.02
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.98
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:14.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.32
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:12.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.12
p-value of test                       :    0.02

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    2.65
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.58
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.17
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.98
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:09.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.47
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:10.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.88e-3
p-value of test                       :    0.9938

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9718.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.75
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.21
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:55.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.86
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.87
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:50.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4314.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12126.33
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.04
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.61
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999911849

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.77
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000037750

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   0.044
p-value of test                       :    0.48

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:37.75

 All tests were passed




Server wird beendet - Lösche Semaphor 102563870.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:42.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7150
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:34.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4227
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:01.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:01.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7105
p-value of test                       :    0.9938


-----------------------------------------------
CPU time used                    :  00:03:53.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:58.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    4.18
p-value of test                       :  7.2e-3

-----------------------------------------------
CPU time used                    :  00:01:46.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    2.50
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:09.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.96
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     175
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:34.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.66
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   19.46
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.31
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.53
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.04
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.76
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:47.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1512.48
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6969.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:46.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.75
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:03.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.91
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.14
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:43.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5032.57
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:20.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45704
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869704
  j =  1                              :        399908594
  j =  2                              :            45700
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46090
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870090
  j =  1                              :        399907825
  j =  2                              :            46080
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  5.0e-3

Anderson-Darling statistic = A2       :    4.89
p-value of test                       :  3.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  2.2e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:29.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:45.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:53.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.32
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.38
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.00
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.59
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.60
p-value of test                       :  3.1e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    4.49
p-value of test                       :  5.3e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   18.63
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.11
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.09
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17276.57
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.57
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.72
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.50
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.11
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.67
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.12
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.79
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.88
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.96
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.20
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.36
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.41
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.33
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.13
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.92
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.05
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.62
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.80
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.77
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.22
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.21
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.57
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.26
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.14
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.31
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.80
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.56
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.86
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.23
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :  -0.082
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:25.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.61
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -1.52
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:17.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 5.72e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.87
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.16
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.58
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:09.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10143.36
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10275.53
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.046
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:44.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.45
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5021.70
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3917.57
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.85
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11520.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.20
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999932681

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.06
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000007384

Normal statistic for number of bits   :   0.058
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   0.080
p-value of test                       :    0.47

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:48.26

 All tests were passed




Server wird beendet - Lösche Semaphor 102957082.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5366
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:43.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:33.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4462
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:54.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:54.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:00.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:00.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:52.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:57.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:45.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     558
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    2.33
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    4.61
p-value of test                       :  4.4e-3

-----------------------------------------------
CPU time used                    :  00:02:10.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:36.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.25
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.09
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.29
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.67
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.85
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.00
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1315.05
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:02:00.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7049.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:44.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.70
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.91
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:05.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.22
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   88.85
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5170.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:57.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45630
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869630
  j =  1                              :        399908744
  j =  2                              :            45622
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45887
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869887
  j =  1                              :        399908230
  j =  2                              :            45879
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:30.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:17.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:00.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:55.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:32.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.73e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.70e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.23e-5
p-value of test                       :    0.9940

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:35.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.84
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.09
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.84
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:48.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.63
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.45
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.01
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.40
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.63
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17492.46
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.49
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.29
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.34
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.24
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.86
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.58
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.20
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.30
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   41.72
p-value of test                       :  7.4e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.94
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.31
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.53
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.35
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.12
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.04
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.82
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.90
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.13
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.68
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.36
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.51
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.34
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.99
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.84
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.30
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  307.04
p-value of test                       :    0.9985


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.78
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.63
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.15
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.05
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:26.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.05
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:23.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.92e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.61e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.54
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.48
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:05.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.26
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10149.78
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:41.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.86
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5068.30
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.35
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4002.91
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11880.04
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11830.59
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.98
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999933578

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.26
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000081799

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :  -0.099
p-value of test                       :    0.54

Sample variance                       :    0.12
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.9e-3

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:28.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 C (L=50, r=25)      7.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 103645210.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5460
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:47.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4445
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:38.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:36.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:58.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:06.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:04.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:57.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:00.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.09
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:11.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    2.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:38.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.95
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.06
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.24
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.79
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.95
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  276.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:53.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.30
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6789.76
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.12
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:16.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.20
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.99
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5134.22
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:04.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45951
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869951
  j =  1                              :        399908100
  j =  2                              :            45947
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45927
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869927
  j =  1                              :        399908148
  j =  2                              :            45923
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:32.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:19.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:51.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:07.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:56.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 3.89e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.34e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:47.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.39
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.53
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.15
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.66
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.60
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.95
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.65
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17219.23
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.15
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.94
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.38
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.47
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.20
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.60
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.98
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.82
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.44
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.59
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.42
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.13
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.84
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.09
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.77
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.87
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.20
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.40
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.17
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.63
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  316.30
p-value of test                       :    0.9950


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.35
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.01
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.78
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.78
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5085.68
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.60
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.78
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.76
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:25.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.13
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:25.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.89e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.75e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 9.20e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.77
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.85
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:05.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.26
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:05.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10151.57
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9828.88
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:04:30.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-3
p-value of test                       :    0.9986

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5049.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4795.24
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4258.91
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.52
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11767.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.20
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:36.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.87
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000030241

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.25
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000061099

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.51
p-value of test                       :  6.1e-3

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:47.22

 All tests were passed




Server wird beendet - Lösche Semaphor 104628250.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1469
p-value of test                       :  2.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334589
  j =  1                              :        599997062
  j =  2                              :             1469
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:52.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4444
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:38.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:37.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:02.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:02.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:53.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:00.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9910

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:12.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    3.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:39.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.09
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.46
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.47
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.37
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.75
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.47
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.97
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.67
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:44.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7082.83
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:43.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.87
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:02.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.73
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.15
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5117.40
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:52.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46129
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870129
  j =  1                              :        399907743
  j =  2                              :            46127
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45882
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869882
  j =  1                              :        399908238
  j =  2                              :            45878
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:28.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:18.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:45.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:34.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 7.44e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:33.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.23
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:48.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   99.44
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.41
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.64
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.56
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.15
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17021.59
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.42
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.56
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.07
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.25
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.76
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.69
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.74
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.32
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.48
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.25
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.84
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.47
p-value of test                       :    0.9942


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.62
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.26
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.30
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.84
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.91
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.46
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.98
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.10
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.68
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.30
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.97
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  435.31
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.65
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.81
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.93
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4885.03
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.36
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.05
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.00
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:24.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.70
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    0.16
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:23.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         : 5.43e-3
p-value of test                       :    0.50

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.03e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.49e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 6.98e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.18
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.08
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.15
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:07.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10210.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:46.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.89
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.63
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3988.81
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.17
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11705.80
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11835.45
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.87
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999943958

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.34
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000028033

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:58.21

 All tests were passed




Server wird beendet - Lösche Semaphor 106037274.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:54.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:38.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:03.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:04.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:55.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:01.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.31
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:12.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.42
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.84
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.31
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.22
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  197.08
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.74
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:46.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1486.15
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:06.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7178.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.89
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:09.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.02
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.12
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:37.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4879.64
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:58.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45788
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869788
  j =  1                              :        399908426
  j =  2                              :            45784
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45414
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869414
  j =  1                              :        399909175
  j =  2                              :            45408
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:29.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:17.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:02.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.00e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.25
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.43
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.35
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.60
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.88
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.27
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:39.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17519.40
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.04
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.20
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.50
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.20
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.16
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.19
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.06
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.72
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.30
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.11
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.96
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.38
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.70
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.18
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.44
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.93
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.79
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.52
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.33
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.92
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.38
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.17
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.54
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.41
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.71
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.50
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.10
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.62
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.90
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.62
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:23.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.55
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:21.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.82
p-value of test                       :    0.97

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 5.28e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.90e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 7.24e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.79
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.74
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.11
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:05.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.65
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:07.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10073.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10021.74
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.021
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:04:18.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.47
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:53.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.46
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:54.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.02
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4422.06
p-value of test                       :  5.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11522.82
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:31.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11863.66
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:31.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.07
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999931268

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.23
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  8000045370

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.16
p-value of test                       :    0.02

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :  5.4e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    5.57
p-value of test                       :  1.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.67
p-value of test                       :    0.9963

Sample variance                       :    0.16
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:37.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 98  HammingIndep, L=300, r=26       5.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 107020314.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1257
p-value of test                       :    0.9983

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334377
  j =  1                              :        599997487
  j =  2                              :             1255
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:49.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4477
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:37.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4483
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:02.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:03.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:54.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:00.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.85
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.24
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    2.15
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:10.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:39.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.90
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.82
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.76
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.81
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.14
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  191.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.02
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6949.13
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:40.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:11.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.74
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.97
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:31.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5217.68
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:57.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46218
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870218
  j =  1                              :        399907567
  j =  2                              :            46212
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45819
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869819
  j =  1                              :        399908368
  j =  2                              :            45807
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:28.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:17.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:45.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:54.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:33.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 5.63e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 4.03e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:34.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:34.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.43
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.02
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.91
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:47.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.40
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.17
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.32
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.45
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17651.80
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.49
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.93
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.18
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.43
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.60
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.73
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.94
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.42
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.94
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.01
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.98
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.86
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.51
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.23
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.83
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.76
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.25
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.34
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.47
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.10
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.18
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.76
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.09
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.59
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.48
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.38
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.22
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.87
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:23.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.65
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -1.88
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:21.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.90
p-value of test                       :    0.97

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.28
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.50
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.31
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:07.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.82
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.06
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:41.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.44
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.50
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.48
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11926.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12339.58
p-value of test                       :  4.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.23
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999804968

Normal statistic for number of bits   :   -1.54
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.30
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999963023

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.52
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.49
p-value of test                       :  6.4e-3

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:47.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 100  HammingIndep, L=1200, r=25      4.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 108232730.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:53.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:47.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:07.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:24.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:26.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:05.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:38.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.58
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.95
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    2.95
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:12.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.33
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:39.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.73
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.68
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.69
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.09
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.89
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.50
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.88
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:34.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:32.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.65
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:23.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7048.37
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:41.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.02
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:03.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.10
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.34
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:34.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5012.32
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:52.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45484
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869484
  j =  1                              :        399909033
  j =  2                              :            45482
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46177
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870177
  j =  1                              :        399907647
  j =  2                              :            46175
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:28.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:24.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 2.88e-3
p-value of test                       :    0.9970

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:12.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.18e-3
p-value of test                       :    0.9955

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:32.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.72e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.19
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:47.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.55
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.71
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.22
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:47.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.59
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.87
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.20
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.88
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.76
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.58
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17588.12
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.62
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.70
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.40
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.19
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.26
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.47
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.59
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.35
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.84
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.73
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.96
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.49
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.64
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.66
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.78
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.12
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.29
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.13
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.49
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.86
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.72
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.81
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.34
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.04
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.53
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.47
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.16
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.86
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.00
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:24.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.33
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -1.40
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:20.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 4.66e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.22e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.23
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.78
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:11.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.27
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:15.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9875.24
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9792.95
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:43.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.01
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:50.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3957.53
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11951.01
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11867.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:30.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.14
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999932798

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.29
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999961529

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:18.98

 All tests were passed




Server wird beendet - Lösche Semaphor 109084698.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5403
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:52.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:39.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:57.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:03.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:54.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:58.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    2.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:12.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:42.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.69
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.07
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.63
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.39
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.10
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.45
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.35
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6884.52
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:41.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.03
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.74
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:02.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.12
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.96
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:35.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5015.34
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:57.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45814
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869814
  j =  1                              :        399908374
  j =  2                              :            45810
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45886
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869886
  j =  1                              :        399908228
  j =  2                              :            45886
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:27.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:17.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:45.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:02.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:54.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:33.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 5.72e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.42e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.062
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:36.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:35.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.90
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.89
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.46
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.85
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.48
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:38.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.59
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.32
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17548.29
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.54
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.08
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.67
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   51.70
p-value of test                       :  8.6e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.58
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.70
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.42
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.06
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.93
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.52
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.68
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.98
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.40
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.29
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.13
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.52
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.92
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.07
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.30
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.06
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.58
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.12
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.40
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.92
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.30
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  449.96
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.83
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.51
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.89
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.52
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:21.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.63
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:19.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.49e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 7.09e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.03
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.14
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.08
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:05.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.67
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:03.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10110.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:40.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4741.10
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:49.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.35
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.58
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11669.29
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11748.97
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.69
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000066604

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.15
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000029374

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.07
p-value of test                       :    0.98

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.04e-3
p-value of test                       :    0.9925

Anderson-Darling statistic = A2       :    4.10
p-value of test                       :  8.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.73
p-value of test                       :    0.9968

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:27.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 R (L=50, r=0)       8.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 110067738.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:56.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:59.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:06.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:09.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:00.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:01.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.95
p-value of test                       :  1.1e-3

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:45.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.33
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:10.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:39.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.94
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.11
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.19
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.40
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.60
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  473.64
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1558.77
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7010.56
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.01
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:14.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.52
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:38.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5138.66
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:52.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46033
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870033
  j =  1                              :        399907937
  j =  2                              :            46027
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45545
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869545
  j =  1                              :        399908913
  j =  2                              :            45539
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:30.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:16.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:04.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.22e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.87e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.71
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.74
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.16
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.17
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.41
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.20
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.45
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17199.30
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.00
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.98
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.83
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.35
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.70
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.46
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.42
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.49
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.66
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.27
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.66
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.20
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.35
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.97
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.73
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.22
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.22
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.24
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.81
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.98
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.04
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.51
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.05
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.83
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.79
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.22
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.75
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.95
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.21
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    1.32
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:21.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.67
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    1.67
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:21.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.18e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 5.07e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.22e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.06
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.17
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.25
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  243.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:05.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.59
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9829.65
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:04:25.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.67
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:55.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.99
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3970.01
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11824.97
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:36.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11770.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:35.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.40
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999937538

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.14
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000116233

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9938

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:09.46

 All tests were passed




Server wird beendet - Lösche Semaphor 110985242.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5479
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:56.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:52.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:01.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:10.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:29.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:28.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:09.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:46.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    3.57
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     965
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.41
p-value of test                       :  5.7e-3

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:11.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.91
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:40.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.65
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.31
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.17
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   28.59
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.05
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.16
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.87
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:00.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6816.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:03.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.17
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.98
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:33.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4940.65
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:51.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46144
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870144
  j =  1                              :        399907715
  j =  2                              :            46138
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45684
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869684
  j =  1                              :        399908636
  j =  2                              :            45676
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  4.8e-3

Kolmogorov-Smirnov- statistic = D-    : 8.61e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:24.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.11e-3
p-value of test                       :    0.9927

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:31.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:21.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:54.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.76e-3
p-value of test                       :    0.9960

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.69
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 5.48e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.31
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.29
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.97
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.43
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:37.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.31
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.53
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.22
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.18
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17451.31
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.53
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.12
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.06
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.98
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.67
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.98
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.03
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.17
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.48
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.31
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.79
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.44
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.18
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.97
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.25
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.28
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.19
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.28
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.05
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.11
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.22
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.61
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  320.23
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.52
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.59
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.72
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.25
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.13
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.97
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.84
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:22.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.61
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    0.16
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:22.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.83
p-value of test                       :    0.97

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.08e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.81e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 7.83e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.46
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.34
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.33
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:04.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.84
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:05.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.17e-3
p-value of test                       :    0.9978

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9633.32
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9908.69
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:42.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4745.27
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.40
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:50.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4271.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.75
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11959.68
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11760.18
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.72
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000045859

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.27
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999967976

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:23.18

 All tests were passed




Server wird beendet - Lösche Semaphor 112164890.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1486
p-value of test                       :  6.0e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334606
  j =  1                              :        599997028
  j =  2                              :             1486
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5457
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:56.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:04.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:04.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:54.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:00.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.83
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    2.57
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:46.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:13.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.62
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.54
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.77
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.79
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.06
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:44.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.46
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:59.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6968.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:43.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.55
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.67
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:03.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.46
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.25
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:35.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4939.22
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:53.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45840
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869840
  j =  1                              :        399908325
  j =  2                              :            45830
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46011
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870011
  j =  1                              :        399907979
  j =  2                              :            46009
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:27.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:17.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:44.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:01.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:59.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:40.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 9.40e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.99e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.93e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:37.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:37.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   99.56
p-value of test                       :  6.0e-3

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   73.22
p-value of test                       :  3.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.13
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:40.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.38
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.77
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17191.79
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.68
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.40
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.09
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.11
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.29
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.38
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.40
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.72
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.91
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.49
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.09
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.87
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.60
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  103.94
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.71
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.51
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.95
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.22
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.42
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.59
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.15
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.52
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.67
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.21
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.54
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5095.41
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.73
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.32
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:22.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.80
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:21.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.087
p-value of test                       :    0.47

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.39e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 5.81e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.92
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.52
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.96
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:05.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:05.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.40
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9875.82
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.22
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4780.29
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4179.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11745.77
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11839.86
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.86
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999928694

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.42
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999951323

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.40e-3
p-value of test                       :    0.9943

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.55
p-value of test                       :  5.4e-3

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    2.73
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:56.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           6.0e-4
 62  WeightDistrib, r = 0            3.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 113082394.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.58

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5432
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:56.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:04.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:53.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:59.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.70
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    3.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:13.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.73
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.76
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.92
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.68
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.66
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1455.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:59.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7003.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:41.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.96
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.41
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:02.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.03
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.45
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:34.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5071.12
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:57.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45846
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869846
  j =  1                              :        399908308
  j =  2                              :            45846
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46135
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870135
  j =  1                              :        399907734
  j =  2                              :            46127
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:27.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:17.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:53.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:32.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.33e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.06e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.38e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:33.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.47
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.54
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.45
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.87
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.81
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.14
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.94
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17609.11
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.89
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.79
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.92
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.15
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.10
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.12
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.68
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.27
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.93
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.68
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.83
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.33
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.31
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.75
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.62
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.27
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.86
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.52
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.07
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.84
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.82
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  436.07
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.64
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.66
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.06
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.61
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.80
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.70
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.41
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:23.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.02
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:22.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.97
p-value of test                       :    0.98

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 6.35e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.71e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.18
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.66
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.79
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:03.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:04.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.66
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.53
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:42.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.32
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.21
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11705.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12088.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.06
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000036742

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.69
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999953675

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.66

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:04.68

 All tests were passed




Server wird beendet - Lösche Semaphor 114098202.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5369
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:57.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:03.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7127
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:54.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:01.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:11.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.46
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    3.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:35.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.08
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.26
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.96
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.61
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.12
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.89
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.30
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.57
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1345.16
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:00.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7109.70
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.97
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.96
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:04.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.00
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.31
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:33.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5028.59
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:51.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46269
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870269
  j =  1                              :        399907470
  j =  2                              :            46253
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45811
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869811
  j =  1                              :        399908382
  j =  2                              :            45803
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:26.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:18.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:54.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.27e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:35.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:35.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.90
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.67
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.05
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.33
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.64
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.28
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.65
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17461.49
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.91
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.85
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.43
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.18
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.22
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.25
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.67
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.69
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.03
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.95
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.10
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.82
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.77
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.88
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.00
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  104.33
p-value of test                       :    0.9963


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.45
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.22
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.01
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.10
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.76
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.45
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.65
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.81
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.55
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5085.32
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.13
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.46
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:34.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.42
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :   0.039
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:21.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.03
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:22.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 9.23e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.91e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.57
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.04
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:05.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.38e-3
p-value of test                       :    0.9921

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10307.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.85
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.57
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:03:41.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.29
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.48
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:50.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3997.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4051.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11696.25
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.30
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999941993

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.88
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000135286

Normal statistic for number of bits   :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.73
p-value of test                       :    0.96

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:00:58.28

 All tests were passed




Server wird beendet - Lösche Semaphor 114950170.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5509
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:56.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:05.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:04.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:55.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:00.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    2.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:11.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:41.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.26
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.18
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.26
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.84
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.88
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.77
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  390.84
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.03
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:00.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7315.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:43.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 7.12e-3
p-value of test                       :    0.9927

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.19
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.05
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:06.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.48
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.81
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4989.35
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9943


-----------------------------------------------
CPU time used                    :  00:02:55.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45815
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869815
  j =  1                              :        399908372
  j =  2                              :            45811
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45558
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869558
  j =  1                              :        399908888
  j =  2                              :            45550
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:26.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:02.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:55.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 2.15e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 8.02e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:37.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.23
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.69
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.60
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.48
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.31
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.81
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17357.71
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.94
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.14
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.22
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.11
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.49
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.57
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.10
p-value of test                       :    0.9924


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.39
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.94
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.09
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.27
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.58
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.81
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.85
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.28
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.61
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.45
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.21
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.12
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.42
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.92
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.12
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.96
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:34.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.00
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.07
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5153.23
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.12
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.73
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.75
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.58
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:21.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.17e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.83
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.48
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.87
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:05.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10021.34
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.32
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:38.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4792.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.03
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.32
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4287.34
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11684.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.72
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.52
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999930080

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.37
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999782945

Normal statistic for number of bits   :   -1.72
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :  -0.051
p-value of test                       :    0.52

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:29.20

 All tests were passed




Server wird beendet - Lösche Semaphor 115965978.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:57.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:06.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:06.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:54.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:00.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.51
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    5.30
p-value of test                       :  2.1e-3

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.95
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:13.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:39.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.90
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.57
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.23
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.15
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.97
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.81
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.01
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.62
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6971.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.31
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:07.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.10
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.11
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5032.90
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:51.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45753
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869753
  j =  1                              :        399908499
  j =  2                              :            45743
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46021
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870021
  j =  1                              :        399907960
  j =  2                              :            46017
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:26.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:16.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.5e-3

Anderson-Darling statistic = A2       :    4.10
p-value of test                       :  8.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  5.1e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:02.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:54.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:32.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.017
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.02
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.32
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.03
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.75
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:37.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.19
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.49
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.78
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.49
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17399.23
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.94
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.32
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.49
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.56
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.85
p-value of test                       :  6.5e-3


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.94
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.51
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.03
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.53
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.73
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.22
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.34
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.60
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.95
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.20
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.91
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.34
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.07
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.07
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   47.46
p-value of test                       :    0.9930


-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.78
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.34
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.84
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.52
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.51
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:34.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.48
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.22
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4813.60
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.51
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  243.35
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.23
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -1.94
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:20.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.90
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:19.87

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 2.41e-3
p-value of test                       :    0.9975

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -2.01
p-value of test                       :    0.98

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.01e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.32
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.43
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.95
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.16
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:05.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10208.15
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10214.03
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:37.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.17
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.34
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3976.63
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11709.79
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.93
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.80
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000005398

Normal statistic for number of bits   :   0.043
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.94
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000033850

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    2.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:16.30

 All tests were passed




Server wird beendet - Lösche Semaphor 116949018.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5529
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:58.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4231
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:43.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4231
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:06.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:07.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:56.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:59.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.32
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:12.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.13
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     123
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:41.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.78
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.89
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.60
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.63
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.19
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.15
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:45.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:59.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7082.61
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:43.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.98
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:05.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.46
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.72
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5118.24
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:51.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45855
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869855
  j =  1                              :        399908293
  j =  2                              :            45849
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908476
  j =  2                              :            45759
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:28.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:18.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:01.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:54.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:31.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.62e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.056
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:35.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.61
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.19
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.17
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.39
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.91
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.72
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.35
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.36
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.94
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17342.54
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.21
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.61
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.27
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.57
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.28
p-value of test                       :    0.9969


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.47
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.19
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.33
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.73
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.77
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.64
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.88
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.51
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.46
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.24
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.63
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.04
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.52
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.43
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.65
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.60
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.34
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.82
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.60
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.22
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.77
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4818.68
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  309.36
p-value of test                       :    0.9959


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.66
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.36
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:21.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.67
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:21.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.73e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.96e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.39
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.36
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.43
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:03.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  160.37
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:04.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.02e-3
p-value of test                       :    0.9914

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9765.15
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.63
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.058
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:40.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5037.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:50.79

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4004.78
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11699.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12080.72
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.72
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000034387

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.43
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999972521

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.15
p-value of test                       :    0.02

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:35.42

 All tests were passed




Server wird beendet - Lösche Semaphor 117964826.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:59.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:43.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:06.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:07.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:58.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:04:00.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:13.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:38.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.14
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.59
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.54
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.68
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.43
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.41
p-value of test                       :    0.9974

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.15
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.00
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.06
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:45.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7251.06
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:43.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.64
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.43
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:03.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.00
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.49
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5029.48
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:50.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46163
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870163
  j =  1                              :        399907675
  j =  2                              :            46161
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45555
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869555
  j =  1                              :        399908894
  j =  2                              :            45547
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:26.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:16.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:54.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:31.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.75e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.69e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:36.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.68
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:48.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.02
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  101.39
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.07
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:40.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.25
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.65
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.05
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17031.38
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.47
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.32
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   45.28
p-value of test                       :  7.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.17
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.55
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.41
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.77
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.10
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.20
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.90
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.12
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.09
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.96
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.88
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.51
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.03
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.06
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.86
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.90
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.14
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.12
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.69
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.97
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.55
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.31
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4863.48
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.43
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.31
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    1.89
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:23.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.53
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:21.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.92e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 8.93e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.12
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.68
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.11
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:03.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.82
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10073.44
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.087
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:40.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.50
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.99
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11640.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11684.11
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:29.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.59
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999979109

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.38
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999949487

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:59.69

 All tests were passed




Server wird beendet - Lösche Semaphor 118947866.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5496
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:57.46

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:42.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:59.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:07.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:08.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:56.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:01.38

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    2.67
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    2.52
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:12.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.17
p-value of test                       :    0.9966

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:45.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   21.48
p-value of test                       :  3.1e-3

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.93
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.94
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.84
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.67
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.26
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.92
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.30
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.00
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7135.10
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.31
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.20
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:03.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.98
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.78
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5115.63
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:51.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46000
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870000
  j =  1                              :        399908005
  j =  2                              :            45990
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46070
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870070
  j =  1                              :        399907864
  j =  2                              :            46062
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:26.94

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:17.39

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:53.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:31.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 4.09e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:34.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.05
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.11
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.55
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   56.05
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.88
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.62
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.03
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17389.67
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.87
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.99
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.80
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.83
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.51
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.97
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.00
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.75
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.96
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.33
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.82
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.61
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.29
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.31
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.79
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.02
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.72
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.93
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.15
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.86
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.55
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.33
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.20
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.71
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.55
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.51
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.22
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.87
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.13
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:22.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.02
p-value of test                       :    0.98

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.04
p-value of test                       :    0.98

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.22e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 7.98e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.21e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.43
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.64
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:04.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.24
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9910.44
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.025
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:37.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.95
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.04
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:51.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.91
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.60
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11577.07
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11831.03
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:30.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.84
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999971729

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.92
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000165223

Normal statistic for number of bits   :    1.31
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:32.36

 All tests were passed




Server wird beendet - Lösche Semaphor 119930906.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:49.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5632
p-value of test                       :  2.2e-3


-----------------------------------------------
CPU time used                    :  00:03:57.26

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:58.53

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:59.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:08.05

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:56.48

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:01.09

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:14.73

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    2.10
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.66
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.33
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.06
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.20
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.37
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  388.89
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:45.36

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.92
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7021.41
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.23
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.76
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:02.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.32
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.95
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4940.37
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:50.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45765
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869765
  j =  1                              :        399908473
  j =  2                              :            45759
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45959
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869959
  j =  1                              :        399908086
  j =  2                              :            45951
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.64

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:26.82

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:17.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:44.55

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:53.72

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:32.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 9.18e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:32.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:32.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.48
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  102.74
p-value of test                       :  3.3e-3

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.73
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.86
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.62
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.21
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.15
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17692.31
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.18
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.09
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    8.69
p-value of test                       :    0.9982


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.19
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.14
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.49
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.84
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.99
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.25
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.43
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.85
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  559.92
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.27
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.75
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.59
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.75
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.47
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.41
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.71
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.94
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4884.29
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.15
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.97
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:34.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.83
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.49
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.86
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.11
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.35
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:34.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.41
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:21.95

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.98
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:21.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :  6.1e-3

Kolmogorov-Smirnov- statistic = D-    : 2.68e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.85
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.03e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.12
p-value of test                       :    0.9998    *****

-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.70
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.71
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.69
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:05.51

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.17
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:07.04

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10211.95
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10021.30
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:38.30

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.99
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5033.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:51.25

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3923.95
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11554.23
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11545.07
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.54
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999854309

Normal statistic for number of bits   :   -1.15
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.93
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999920030

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n90, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:34.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 85  Fourier3, r = 27                0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 120913946.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:43.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:37.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:35.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:03.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:03.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:56.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:02.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.48
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.95
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.40
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    5.75
p-value of test                       :  1.3e-3

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:07.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.49
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:43.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.88
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.69
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.60
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.64
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.24
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.69
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.47
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:08.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6927.14
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:49.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.36
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.11
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:14.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.48
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:47.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.50
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.23
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:10.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45943
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869943
  j =  1                              :        399908115
  j =  2                              :            45941
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45711
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869711
  j =  1                              :        399908581
  j =  2                              :            45705
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:29.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  8.0e-3

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  8.8e-3

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 3.03e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.16
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.17
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:53.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.75
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.70
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.17
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.00
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17478.34
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.93
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.90
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.13
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.70
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.84
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.91
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.58
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.36
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.54
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.72
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  202.59
p-value of test                       :  1.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.65
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.52
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.32
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.51
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.82
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.93
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.97
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.07
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.57
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.35
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5220.98
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.19
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.26
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.24
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.21
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4882.54
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.25
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.45
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.50
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:26.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.93
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:25.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.82
p-value of test                       :    0.97

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.26e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.76e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.58
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.28
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.57
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:07.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.60
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10084.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9884.86
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:04:19.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.38
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:53.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.60
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.56
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.09
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11883.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:36.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11987.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:38.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.85
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000027433

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.99
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000091894

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:16:58.52

 All tests were passed




Server wird beendet - Lösche Semaphor 101580800.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:47.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:38.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:37.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:03.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:01.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:03.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    2.08
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    2.93
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:15.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.58
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:45.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.40
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.53
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.54
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  264.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.29
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.83
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6983.39
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:51.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.67
p-value of test                       :  4.7e-3

Kolmogorov-Smirnov- statistic = D-    : 8.51e-3
p-value of test                       :    0.9912

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   13.96
p-value of test                       :    0.9944

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.12
p-value of test                       :    0.9999    *****

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:00.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.04
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.66
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5154.15
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:56.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46210
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870210
  j =  1                              :        399907583
  j =  2                              :            46204
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45881
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869881
  j =  1                              :        399908244
  j =  2                              :            45869
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:24.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:16.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.34e-3
p-value of test                       :    0.9949

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:57.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:38.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.64e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.66e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:38.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.65
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.25
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.08
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.85
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.48
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:40.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17290.06
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.14
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.38
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.37
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.53
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.50
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.30
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.04
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.22
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.26
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  195.80
p-value of test                       :  3.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.94
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.99
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.32
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.65
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.14
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.98
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.23
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.94
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.89
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.32
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5189.14
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.30
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.26
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.01
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.25
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4824.13
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.47
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.19
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.46
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   0.048
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.25
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   -2.14
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:26.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    2.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.91e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.58
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.19
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 9.26e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  154.21
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:02:08.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:08.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10131.05
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9869.83
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:40.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4695.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.63
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4223.97
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.51
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11965.73
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.70
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.80
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999967541

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.16
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999973943

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:03.30

 All tests were passed




Server wird beendet - Lösche Semaphor 103481344.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5376
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:47.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:38.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:37.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:03.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:00.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:05.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:15.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.36
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:42.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.72
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   19.68
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.27
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.24
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.48
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.87
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  192.01
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.44
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1334.40
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:03.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7105.59
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:51.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.57
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.55
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:06.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.38
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:34.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5116.15
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:58.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46295
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870295
  j =  1                              :        399907411
  j =  2                              :            46293
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45791
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869791
  j =  1                              :        399908419
  j =  2                              :            45789
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.73e-3
p-value of test                       :    0.9928

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:25.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:18.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:02.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.45e-3
p-value of test                       :    0.9985

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:39.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.63e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : 2.21e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.013
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:44.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.65
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.28
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.71
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.56
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.01
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.48
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:40.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17675.47
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.69
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.04
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.15
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.36
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.36
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.87
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.41
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.40
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.48
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.88
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.96
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.12
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.99
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.89
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.74
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.04
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.46
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.96
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.84
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.92
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.79
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.01
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.62
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.27
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.06
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4810.21
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.96
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.11
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.06
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :    1.33
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:26.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.01
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:25.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.73e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.11e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.15
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.73
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.74
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:08.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.05
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10030.19
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:04:15.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.04
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.90
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4420.45
p-value of test                       :  5.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.05
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11807.12
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11904.73
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.60
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000143725

Normal statistic for number of bits   :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.38
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999914999

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   0.098
p-value of test                       :    0.46

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -1.91
p-value of test                       :    0.97

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   0.012
p-value of test                       :    0.50

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:26.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 97  HammingIndep, L=300, r=0        5.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 104431616.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:52.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5354
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:49.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:37.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4220
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:02.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:06.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7177
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:57.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:01.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.42
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    2.43
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:13.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:45.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.63
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   37.42
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.54
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.34
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.74
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.63
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.92
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1475.34
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7086.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:51.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.92
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:58.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.56
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.38
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5040.98
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:53.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45786
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869786
  j =  1                              :        399908432
  j =  2                              :            45778
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45779
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869779
  j =  1                              :        399908444
  j =  2                              :            45775
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
p-value of test                       :    0.9931

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:26.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:17.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:46.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.73e-3
p-value of test                       :    0.9943

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:38.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.071
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:33.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.80
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.79
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.26
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.19
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.35
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.01
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.90
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17352.34
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:55.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.60
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.45
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.37
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.18
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.69
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.05
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.51
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.25
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.86
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.09
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.15
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.02
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.39
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.94
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.38
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.17
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.46
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.36
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.13
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.60
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.94
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.23
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.27
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.29
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.36
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.40
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:25.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.33
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:24.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 8.56e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.68e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.78
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.93
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.48
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:04.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.61
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10052.71
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.68
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:43.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.35
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.79
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.61
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11611.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12056.66
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.68
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999937946

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.72
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000009052

Normal statistic for number of bits   :   0.072
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.18
p-value of test                       :    0.99

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:27.53

 All tests were passed




Server wird beendet - Lösche Semaphor 105381888.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5457
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:50.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4199
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:39.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:37.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:54.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:01.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:55.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7161
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:02.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.97
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.86
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:14.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:42.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.54
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.59
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.93
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.72
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.39
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.11
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1382.58
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6973.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:52.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.68
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:57.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.17
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   89.89
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5035.63
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:11.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46117
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870117
  j =  1                              :        399907770
  j =  2                              :            46109
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45648
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869648
  j =  1                              :        399908704
  j =  2                              :            45648
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:26.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:18.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:38.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.09e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.032
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:34.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:34.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.48
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.83
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.72
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.81
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.87
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17727.93
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.55
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.23
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.67
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.08
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.88
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.46
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.31
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.00
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.90
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.06
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.27
p-value of test                       :    0.9955


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.19
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.37
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.24
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.83
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.81
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.82
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.81
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.28
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.78
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.31
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4887.13
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  432.82
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.21
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.19
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.03
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.78
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  245.38
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.04
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -1.80
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:25.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.68
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:25.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 9.53e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.37
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.32
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.82
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:07.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.78
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:08.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10024.12
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9959.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:44.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:46.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4003.16
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.57
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11843.53
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11944.83
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.43
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999990905

Normal statistic for number of bits   :  -0.072
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.40
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999956273

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:00.75

 All tests were passed




Server wird beendet - Lösche Semaphor 106299392.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:51.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5312
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:52.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:37.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:01.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:05.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:56.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:00.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:13.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.76
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.08
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.19
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.48
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.85
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  197.09
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.75
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:46.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1350.15
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6902.83
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:51.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.22
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:57.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.55
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.89
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4893.21
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:17.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45535
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869535
  j =  1                              :        399908930
  j =  2                              :            45535
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46030
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870030
  j =  1                              :        399907943
  j =  2                              :            46024
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:26.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 7.84e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:22.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:33.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.18
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.17
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.99
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.99
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.89
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.30
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.05
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17504.95
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.78
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.80
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.85
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.44
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.78
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.88
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.85
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.13
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.85
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.42
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.60
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.13
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.42
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.23
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.34
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.90
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.38
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.70
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.78
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.50
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.12
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5053.19
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.36
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.56
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.23
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.79
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.42
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.89
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.30
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:21.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.82
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:23.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.48
p-value of test                       :    0.9934

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    2.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.76e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.97
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.93
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:06.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.2e-3

Anderson-Darling statistic = A2       :    3.99
p-value of test                       :  9.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  250.31
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:02:05.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9982.30
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9882.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.037
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.018
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:42.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5038.88
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.44
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4293.27
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3933.50
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.72
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11715.66
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.33
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999981533

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.64
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000020677

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:23.93

 All tests were passed




Server wird beendet - Lösche Semaphor 107282432.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5339
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:51.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:39.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:38.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:01.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:04.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:56.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:00.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.13
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:12.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:41.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.80
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.61
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.78
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.81
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.84
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.46
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.13
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.80
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1300.45
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:02:06.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7188.80
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.17
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:58.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.00
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.86
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4985.52
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:02.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45623
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869623
  j =  1                              :        399908756
  j =  2                              :            45619
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46119
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870119
  j =  1                              :        399907769
  j =  2                              :            46105
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:26.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:17.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:59.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:37.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.90e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.035
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.62
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.76
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.19
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.83
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.24
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.57
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17516.45
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.16
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.22
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.64
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.11
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.41
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.43
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.56
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.80
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.19
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.06
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.75
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.83
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.68
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.44
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.03
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.45
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.51
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.09
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.84
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5053.92
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.96
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.69
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.29
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.44
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.11
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.37
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.43
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.25
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:25.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.20
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:23.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 9.78e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.94e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 9.58e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.19
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.30
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.92
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:04.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.1e-3

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10273.16
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10059.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:44.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4814.42
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:45.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.41
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4252.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11732.07
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11764.61
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.23
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000004747

Normal statistic for number of bits   :   0.038
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.36
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000003697

Normal statistic for number of bits   :   0.029
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:09.22

 All tests were passed




Server wird beendet - Lösche Semaphor 108232704.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:49.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7188
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:38.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4213
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:03.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:55.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:57.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    3.15
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     990
p-value of test                       :  1.6e-3

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.16
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     333
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:10.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    2.46
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     120
p-value of test                       :    0.9934

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:42.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.72
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.94
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.83
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:45.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.51
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:08.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7050.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.67
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.83
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:02.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.07
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.98
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:30.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5150.25
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:59.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46194
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870194
  j =  1                              :        399907613
  j =  2                              :            46192
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46068
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870068
  j =  1                              :        399907865
  j =  2                              :            46066
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:26.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:16.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :  2.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 8.28e-4
p-value of test                       :    0.9992    *****

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:56.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.45e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 8.90e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.44
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.44
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.46
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.87
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.55
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 7.04e-3
p-value of test                       :    0.9925

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17763.01
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.36
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.33
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.42
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.96
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.58
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.62
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.80
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.75
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.12
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.88
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.08
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.45
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.95
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.68
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.87
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.51
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  437.48
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.95
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.89
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.68
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.96
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4877.08
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.97
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.32
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.88
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.93
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4841.40
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.09
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.46
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.51
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:22.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.13
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.45e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 7.48e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.88
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.60
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:05.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:07.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9832.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:43.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.55
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:45.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.42
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.50
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11929.92
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12043.19
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.49
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000040783

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.70
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000099907

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:02.59

 All tests were passed




Server wird beendet - Lösche Semaphor 109084672.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5366
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:50.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:04.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:03.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:54.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:59.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.67
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.92
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:11.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:39.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.20
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.62
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.33
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.38
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.18
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.03
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.32
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.37
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7001.92
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:01.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.26
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.76
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5030.26
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:02.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45690
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869690
  j =  1                              :        399908623
  j =  2                              :            45684
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46107
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870107
  j =  1                              :        399907788
  j =  2                              :            46103
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:26.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:17.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:58.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.29e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.70e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 3.60e-4
p-value of test                       :  5.6e-3

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.085
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.87
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.72
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.80
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.02
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.03e-3
p-value of test                       :    0.9925

Anderson-Darling statistic = A2       :    4.54
p-value of test                       :  5.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16871.59
p-value of test                       :    0.9987



-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.47
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.63
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.25
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.91
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.55
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.90
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.06
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.95
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.65
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.68
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.48
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.38
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.07
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.95
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.37
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.77
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.88
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.70
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.88
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.29
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  319.09
p-value of test                       :    0.9931


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4775.13
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.22
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.13
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.27
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.55
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.90
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.23
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.43
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.00
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:24.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.62
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:22.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.4e-3

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.96e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 8.52e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.55
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.76
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.70
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:07.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.73
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.25
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:40.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5034.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:45.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.55
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4012.89
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.22
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11720.18
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.81
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.65
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999914678

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.56
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999854072

Normal statistic for number of bits   :   -1.15
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.91

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.078
p-value of test                       :    0.47

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:12.34

 All tests were passed




Server wird beendet - Lösche Semaphor 110002176.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5650
p-value of test                       :  1.0e-3


-----------------------------------------------
CPU time used                    :  00:03:51.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:40.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:57.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:04.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7480
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:55.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:59.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.14
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.05
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.29
p-value of test                       :  6.6e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    2.43
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:11.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.60
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.83
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.28
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.61
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.89
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.83
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.27
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.78
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:06.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7100.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.69
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:02.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.28
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.46
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:31.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4962.43
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:10.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45803
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869803
  j =  1                              :        399908400
  j =  2                              :            45791
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45708
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869708
  j =  1                              :        399908588
  j =  2                              :            45700
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:26.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:17.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:59.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:00.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:37.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.01
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.17
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  101.52
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.97
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.80
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.73
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17664.79
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.33
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.50
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.19
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.20
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.71
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.02
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.09
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   43.02
p-value of test                       :  9.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.72
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.49
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.88
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.31
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.45
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.27
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.41
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.87
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.35
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.77
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.36
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  324.51
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.77
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.85
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  311.65
p-value of test                       :    0.9946


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.92
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.97
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.89
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.46
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.64
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.83
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:22.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.61
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 2.52e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.95e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.32
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.42
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.94
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9918.03
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.44
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:42.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.06
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:45.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3986.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3981.73
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11843.54
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.00
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.96
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000041242

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.93
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000008740

Normal statistic for number of bits   :   0.069
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.31
p-value of test                       :    0.99

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:48.20

 All tests were passed




Server wird beendet - Lösche Semaphor 111017984.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:51.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1226
p-value of test                       : 1 -  7.5e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334346
  j =  1                              :        599997548
  j =  2                              :             1226
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:54.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:05.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:56.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:03.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.30
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    2.41
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     949
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    2.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:12.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.13
p-value of test                       :    0.9997    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.26
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.10
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.00
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.38
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.66
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.42
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:21.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6808.46
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:51.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:20.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.88
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:47.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.87
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4939.71
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:08.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46035
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870035
  j =  1                              :        399907933
  j =  2                              :            46029
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908144
  j =  2                              :            45925
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:31.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:20.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:59.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:38.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.58e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.014
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.045
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:51.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.64
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.46
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.89
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:52.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.37
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17676.79
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.51
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.27
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.77
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.34
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.02
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.38
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.19
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.27
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.59
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.81
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.67
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.41
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.81
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.01
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.47
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.40
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.27
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.00
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.32
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.75
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5137.28
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.52
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.37
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.79
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.57
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.27
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.06
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.39
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.90
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    1.68
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:22.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.23
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -1.15
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:24.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.81e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 6.69e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.53
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.17
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.01
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:05.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.26
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:05.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10154.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9813.95
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.100
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:19.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.77
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.82
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:59.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.69
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.50
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11987.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11850.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:36.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.57
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000010822

Normal statistic for number of bits   :   0.086
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.19
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999997526

Normal statistic for number of bits   :  -0.020
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:19.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21          1 -  7.5e-5
 25  ClosePairs mNP1, t = 16         0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 111968256.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5469
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:53.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:05.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:05.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:56.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:00.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    4.71
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     644
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.15
p-value of test                       :    0.9986

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:12.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:41.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.10
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.78
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.28
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.37
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.31
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:45.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1488.27
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:06.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6816.78
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.26
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:01.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.79
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.86
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5081.27
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:02.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45608
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869608
  j =  1                              :        399908792
  j =  2                              :            45592
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45765
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869765
  j =  1                              :        399908474
  j =  2                              :            45757
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:26.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:03.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:58.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.59e-3
p-value of test                       :    0.9925

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:39.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 8.22e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.40e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.038
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:35.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.88
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.68
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.71
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.16
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.11
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.99
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.47
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.72
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.14
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17727.28
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.28
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.12
p-value of test                       :    0.9918


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.17
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.16
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.61
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.50
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.20
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.80
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.19
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.31
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.87
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.03
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.86
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.70
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.65
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.59
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.24
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.97
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.60
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.02
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4849.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  452.17
p-value of test                       :  5.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.81
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.21
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.19
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.15
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.50
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.93
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.41
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:21.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.43
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:20.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.92

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.69e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 7.50e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.04e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.61
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.88
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 9.88e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:06.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.38
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:05.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9844.98
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.6e-3

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10258.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:39.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5007.59
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3998.26
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4312.75
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12054.01
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11935.01
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.82
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000066133

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.51
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999826811

Normal statistic for number of bits   :   -1.37
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-3
p-value of test                       :    0.9983

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.94
p-value of test                       :    0.03

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:57.73

 All tests were passed




Server wird beendet - Lösche Semaphor 113278976.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:50.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:54.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:07.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:07.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7530
p-value of test                       :  7.0e-3


-----------------------------------------------
CPU time used                    :  00:04:00.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:02.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.86
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    3.28
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     845
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    2.59
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     550
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:12.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9930

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.71
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.99
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.62
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.15
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.03
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1474.58
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:07.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7030.79
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.65
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.21
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:06.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.14
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.79
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:36.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5022.78
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:03.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45476
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869476
  j =  1                              :        399909052
  j =  2                              :            45468
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908164
  j =  2                              :            45915
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:28.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:18.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:04.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:37.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 6.65e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.83
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.32
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.69
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.79
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.53
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  100.69
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17356.28
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.63
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.91
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.92
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.66
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.59
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.34
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.68
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.58
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.20
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.42
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.20
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.31
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.67
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.56
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.16
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.69
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.91
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.88
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.49
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.61
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.95
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.46
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.77
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.26
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.63
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.86
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4840.88
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.62
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.41
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.32
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    1.08
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:22.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.80
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 3.77e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.38e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.73e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.94
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.76
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.64
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:08.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.68
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:07.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.81e-3
p-value of test                       :    0.9928

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10344.16
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9889.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:04:09.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4776.99
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:51.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.86
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:52.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4209.56
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.33
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11847.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:29.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.45
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999951149

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.74
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999862388

Normal statistic for number of bits   :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.059
p-value of test                       :    0.48

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :  -0.032
p-value of test                       :    0.51

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:16.67

 All tests were passed




Server wird beendet - Lösche Semaphor 114130944.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:01.62

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5376
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:53.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:04.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:05.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:57.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:03.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.04
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:14.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.59
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.24
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.24
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.97
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.67
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.17
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  379.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:09.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7032.36
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.37
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:20.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.79
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.38
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4993.69
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:54.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46323
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870323
  j =  1                              :        399907355
  j =  2                              :            46321
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45579
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869579
  j =  1                              :        399908846
  j =  2                              :            45571
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:31.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:20.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:03.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:39.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.40e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 7.99e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.059
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.34
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.20
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.35
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.46
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:51.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.10
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.71
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.37
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.70
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17424.71
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.34
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.51
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.25
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.25
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.55
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   60.36
p-value of test                       :  4.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.17
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.09
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.66
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.99
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.17
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.13
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.57
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.54
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.62
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.68
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.13
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.47
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.73
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.23
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.62
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5155.61
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.76
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.30
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.17
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.41
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5131.30
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.10
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.19
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.34
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :    1.33
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:21.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.61
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   0.030
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 7.87e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 9.17e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.55
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.45
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:07.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.57
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:07.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.67
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-3
p-value of test                       :    0.9978

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.6e-3

Anderson-Darling statistic = A2       :    4.26
p-value of test                       :  6.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10405.23
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.062
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:04:21.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.54
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.65
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.33
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.06
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11954.21
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:38.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.41
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000148081

Normal statistic for number of bits   :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.60
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999992474

Normal statistic for number of bits   :  -0.059
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.86
p-value of test                       :    0.03

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:11.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:19.52

 All tests were passed




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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:27.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1257
p-value of test                       :    0.9983

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334377
  j =  1                              :        599997486
  j =  2                              :             1257
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5555
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:51.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:56.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:05.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:06.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:58.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:00.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.42
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:14.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:45.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.15
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.30
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.44
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.18
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.45
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.32
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1496.61
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:04.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7218.93
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.68
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:01.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.06
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.67
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4929.52
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:58.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46269
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870269
  j =  1                              :        399907465
  j =  2                              :            46263
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45899
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869899
  j =  1                              :        399908208
  j =  2                              :            45887
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:27.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:16.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:02.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:59.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.79e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:40.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:36.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.37
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.04
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.28
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.61
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.21
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.60
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.00
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17603.12
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.43
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.70
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.53
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.03
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.12
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.40
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.43
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.74
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.75
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.28
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.88
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.66
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.99
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.46
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.45
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.14
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.32
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.76
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.73
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.27
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.99
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.91
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5153.28
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.30
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.56
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.72
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.82
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.30
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.14
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.53
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.54
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:22.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.58
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:23.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.76e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.41e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.99
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.27
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:03.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.89
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:05.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10067.03
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10122.26
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:43.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.50
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4667.78
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:47.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.20
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11585.69
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11767.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.29
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000054217

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.42
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000030826

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:34.87

 All tests were passed




Server wird beendet - Lösche Semaphor 116490240.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:48.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:27.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5413
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:54.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:05.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:07.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:57.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:02.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:13.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:42.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.47
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.53
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.27
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.33
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.38
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.02
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.19
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.09
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:45.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.32
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:15.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7336.82
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.51
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:01.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.56
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.21
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5160.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:59.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45754
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869754
  j =  1                              :        399908497
  j =  2                              :            45744
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45814
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869814
  j =  1                              :        399908378
  j =  2                              :            45802
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:26.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:17.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:45.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:59.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:03.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 9.46e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.031
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.058
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:37.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.44
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.92
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.36
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.64
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.68
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   13.92
p-value of test                       :  9.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.51
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17445.28
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.38
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.81
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.16
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.75
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.93
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.88
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.23
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.90
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.61
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.96
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.94
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.25
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.34
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.15
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.61
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.91
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.10
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.04
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.90
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.69
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.53
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5262.63
p-value of test                       :  4.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.61
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.53
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.34
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.72
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.27
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.95
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.71
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.64
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:23.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.27
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:23.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.85e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.87
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.27
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.39
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:03.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.96
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:04.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10083.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:41.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:47.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.05
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3975.13
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.47
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11547.34
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.21
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.68
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000101407

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.51
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000128356

Normal statistic for number of bits   :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.99
p-value of test                       :    0.02

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:53.02
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 70  MatrixRank, L=5000              9.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 117473280.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5431
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:54.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:57.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:58.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:05.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:58.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:02.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     939
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    2.56
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    2.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:15.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:43.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.00
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.14
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.67
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.94
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.93
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.93
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:45.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1358.81
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7095.51
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:02.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.67
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.18
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5176.94
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:59.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45698
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869698
  j =  1                              :        399908606
  j =  2                              :            45694
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45817
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869817
  j =  1                              :        399908368
  j =  2                              :            45813
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:26.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:17.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:59.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:58.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.40e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.90e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.35
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   36.42
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.29
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.62
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 7.63e-3
p-value of test                       :    0.9918

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.48
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.88
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17383.22
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.58
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.28
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.04
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.67
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.84
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   45.57
p-value of test                       :  7.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.13
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.30
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.34
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.26
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.53
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.98
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.84
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.45
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.72
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.90
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.36
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.25
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.80
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.77
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4834.78
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.36
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.81
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.26
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.95
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.49
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.03
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.35
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.39
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:23.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.66
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:23.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.11e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.76e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.58e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.89e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.09
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.67
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:05.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:06.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.07
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9832.94
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:39.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.52
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:46.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4736.03
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.93
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3945.76
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.16
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11735.14
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.12
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000004897

Normal statistic for number of bits   :   0.039
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.12
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000033388

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.63
p-value of test                       :    0.05

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:28.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 60  WeightDistrib, r = 20           0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 118489088.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5486
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:54.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:40.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:05.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7505
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:05.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:58.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:02.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:12.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    2.11
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     122
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:44.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.01
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.17
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.20
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.72
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.61
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.34
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.72
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.30
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:45.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.57
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:06.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7200.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.65
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:01.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.46
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.70
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5047.53
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:58.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46072
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870072
  j =  1                              :        399907857
  j =  2                              :            46070
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46151
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870151
  j =  1                              :        399907700
  j =  2                              :            46147
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:26.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:19.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:03.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:58.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.41e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 5.59e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:38.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.41
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.57
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.95
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.67
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.64
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.98
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.17
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.82
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.3e-3

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  161.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:39.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17321.38
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.07
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.76
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.12
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.94
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.81
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.57
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.16
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.41
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.42
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.38
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.08
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.06
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.63
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.02
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  117.19
p-value of test                       :  1.0e-3


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.42
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.62
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.91
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.08
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.79
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.79
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.66
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.38
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.68
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.99
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.08
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.67
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.97
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:34.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.35
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -1.23
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.46
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:23.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    2.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.26e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.16
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.91
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.47
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:04.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.43
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:04.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.11e-3
p-value of test                       :    0.9913

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10325.83
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10157.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:40.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9915

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.38
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3984.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11733.17
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.79
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.47
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999971639

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.69
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999896522

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    2.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:26.35

 All tests were passed




Server wird beendet - Lösche Semaphor 119406592.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1256
p-value of test                       :    0.9984

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334376
  j =  1                              :        599997488
  j =  2                              :             1256
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5403
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:56.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:05.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:59.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:02.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.33
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    2.24
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.24
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.30
p-value of test                       :  6.6e-3

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:13.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.68
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.96
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.73
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   83.07
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.79
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.92
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.03
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:45.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1505.21
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7171.42
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:25.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.21
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.61
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:31.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5141.44
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:58.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45463
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869463
  j =  1                              :        399909077
  j =  2                              :            45457
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45814
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869814
  j =  1                              :        399908376
  j =  2                              :            45806
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:26.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:38.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:24.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 3.28e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.19
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.49
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.35
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.30
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.77
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.30
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.91
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.72
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.12
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17376.54
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.19
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.83
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.57
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.04
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    4.65
p-value of test                       :    0.9986


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.14
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.74
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.86
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.70
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.85
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.47
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.68
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  580.99
p-value of test                       :  7.0e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.54
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.36
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.86
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.42
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.88
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.40
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.31
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.54
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.82
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4857.40
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.74
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.11
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.95
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.14
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.41
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.55
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.86
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:23.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.78
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  2.0e-3

Anderson-Darling statistic = A2       :    3.84
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.32
p-value of test                       :    0.01

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.40e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 2.17e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.74e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.68
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.87
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.42
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:04.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10022.94
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9841.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:41.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.18
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.14
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.93
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12267.95
p-value of test                       :  2.2e-3

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11593.57
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.29
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999927368

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.08
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000005722

Normal statistic for number of bits   :   0.045
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:39.18

 All tests were passed




Server wird beendet - Lösche Semaphor 120422400.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  4.5e-3


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5381
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:55.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:41.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4477
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:57.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:58.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:05.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:06.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:58.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:02.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     641
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.99
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    2.43
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    4.64
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:02:15.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9947


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    3.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.60
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.37
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.26
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.72
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.95
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  372.69
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1371.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7171.21
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.20
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:59.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.96
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.96
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4883.20
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:57.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45674
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869674
  j =  1                              :        399908655
  j =  2                              :            45668
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45818
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869818
  j =  1                              :        399908367
  j =  2                              :            45812
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:26.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:59.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-5
p-value of test                       :    0.9950

Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 8.70e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:35.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.71
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.32
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.85
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.22
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.40
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.67
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.26
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.42
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.95
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:39.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17706.45
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.98
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.33
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.90
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.87
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.29
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.64
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.13
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.78
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.35
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.42
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.98
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  574.19
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.07
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.43
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.67
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.10
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.20
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.41
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.64
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.90
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.17
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5086.84
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.98
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.32
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.25
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.49
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.58
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.29
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:33.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.70
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:17.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.61
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:18.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.73e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 6.31e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.01e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.51
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.90
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.88
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.43
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:59.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10285.29
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10157.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:30.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4755.00
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.47
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4238.63
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.11
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11676.48
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12050.88
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.40
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000008518

Normal statistic for number of bits   :   0.067
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.74
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000013087

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    2.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:59:08.89

 All tests were passed




Server wird beendet - Lösche Semaphor 121438208.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1255
p-value of test                       :    0.9986

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334375
  j =  1                              :        599997490
  j =  2                              :             1255
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:41.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:35.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:34.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:54.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:00.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:00.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:52.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:58.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.78
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    2.35
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     655
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    2.29
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:13.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.04
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    2.80
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:35.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.12
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.15
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.87
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.12
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.51
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.83
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.75
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7073.37
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.20
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:02.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.71
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.07
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4914.34
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:59.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45553
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869553
  j =  1                              :        399908897
  j =  2                              :            45547
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908188
  j =  2                              :            45903
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:29.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9988

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:59.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:53.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:35.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:34.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.79
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.84
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.90
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.79
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.35
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.01
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.95
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.37
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.7e-3

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17859.52
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.18
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.88
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.62
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.60
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.03
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.84
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.91
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.47
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.84
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.74
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.16
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.64
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.46
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.84
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.98
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.10
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.72
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.33
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.14
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.04
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.39
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.03
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.13
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.84
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.63
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.75
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.09
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.23
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.16
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.49
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.19
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :   -1.22
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:26.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.75
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:19.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
p-value of test                       :    0.9925

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.83e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.35
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.96
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.32
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:05.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.31
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:09.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9815.95
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9852.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:44.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.85
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:47.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.41
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.57
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11653.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11656.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.13
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999968504

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.59
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000063568

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.94
p-value of test                       :    0.97

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.92

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    6.46
p-value of test                       :  6.4e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -3.34
p-value of test                       :    0.9996    *****

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:00.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 106  AutoCor, d=3, r=27              0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 101613569.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:46.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:46.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:58.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4452
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:09.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:26.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:28.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7158
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:18.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:49.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     643
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:11.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.06
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:39.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.12
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.38
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.25
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.71
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  189.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.12
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:32.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1400.70
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:34.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7238.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:36.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:04.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.46
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.98
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5176.41
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:01.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45546
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869546
  j =  1                              :        399908915
  j =  2                              :            45532
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45596
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869596
  j =  1                              :        399908811
  j =  2                              :            45590
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:35.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:26.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:52.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:08.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 9.20e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:32.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:33.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:48.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.03
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:34.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:35.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.86
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:35.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:34.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.04
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.41
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:11.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:12.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17490.84
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.23
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.03
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.85
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.79
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.09
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.52
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.86
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.84
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.02
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.70
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.88
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.42
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.75
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.33
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.65
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.80
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.49
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.26
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.21
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.09
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.30
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.46
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.65
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.92
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.82
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4861.09
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.56
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.76
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.62
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -1.21
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:23.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.15
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:19.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.17

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.57e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 8.22e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.06
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.93
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:08.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.69
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:08.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.61
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.081
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:47.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.84
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5146.67
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:01:48.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3983.90
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11730.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.44
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999974924

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.78
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000043753

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.050
p-value of test                       :    0.52

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:16:52.37

 All tests were passed




Server wird beendet - Lösche Semaphor 102694913.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5362
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:46.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4214
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:37.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:35.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:54.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:54.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:01.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:01.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:53.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:58.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:11.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:39.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.76
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.08
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.57
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.60
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.78
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.28
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.21
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1347.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6803.55
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.82
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.62
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:03.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.72
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.23
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5046.64
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:56.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45830
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869830
  j =  1                              :        399908347
  j =  2                              :            45816
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45552
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869552
  j =  1                              :        399908899
  j =  2                              :            45546
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:29.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:17.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:46.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.81
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:38.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.21e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.34e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.056
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:33.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:34.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.81
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.45
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.07
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.96
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:41.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.79
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.25
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.98
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.60
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.57
p-value of test                       :  6.4e-4    *****

Anderson-Darling statistic = A2       :    4.91
p-value of test                       :  3.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17897.13
p-value of test                       :  6.5e-3



-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.90
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.86
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.72
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.19
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.23
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.28
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.03
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.97
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.84
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.86
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.88
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.02
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.91
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.12
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  107.89
p-value of test                       :  6.2e-3


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.29
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.68
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.78
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.48
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.82
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.52
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.79
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5206.35
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.94
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.69
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.64
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.07
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4805.28
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.14
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.31
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -1.25
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:25.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.75
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:21.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.18e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.99e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.59
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.91
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.51
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:08.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.55
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10152.58
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:49.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.99
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:47.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.60
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11922.90
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.85
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.99
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000077590

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.59
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999781802

Normal statistic for number of bits   :   -1.73
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:46.02

 All tests were passed




Server wird beendet - Lösche Semaphor 103677953.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:50.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7154
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:35.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:54.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:01.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7521
p-value of test                       :  9.3e-3


-----------------------------------------------
CPU time used                    :  00:03:00.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:52.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:57.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    2.41
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:10.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:38.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.26
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.29
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.86
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.58
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.33
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.54
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.83
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.32
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:45.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1388.84
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6960.78
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.01
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.94
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:03.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.26
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.17
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5079.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:56.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45719
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869719
  j =  1                              :        399908566
  j =  2                              :            45711
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46114
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870114
  j =  1                              :        399907773
  j =  2                              :            46112
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:29.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:17.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:45.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:58.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:36.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.75e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 5.46e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.43
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.93
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9944

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.33
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  100.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17444.07
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.16
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.30
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.79
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.66
p-value of test                       :    0.9958


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.40
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.87
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.88
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.84
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.92
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.95
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.43
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.47
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.05
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.74
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.30
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.50
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.12
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.50
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.01
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.05
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.39
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.92
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.19
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.43
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.70
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.85
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.36
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.81
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.16
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.77
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :    1.18
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:24.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.94
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :  -0.100
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.08
p-value of test                       :    0.98

Sample variance                       :    2.93
p-value of test                       :  1.8e-3

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.50e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.09e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.30
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.92
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.64
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:04.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.80
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:06.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.88
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10136.72
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:46.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4777.82
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.00
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.07
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11898.11
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11570.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.39
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000180106

Normal statistic for number of bits   :    1.42
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.70
p-value of test                       :    0.9903


-----------------------------------------------
Total number of bits:  7999968843

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:25.00

 All tests were passed




Server wird beendet - Lösche Semaphor 104693761.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5338
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:54.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:37.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:54.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:00.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:01.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:53.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:58.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.51
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:46.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    2.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.95
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:09.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:37.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.72
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.85
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.07
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.56
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.90
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1376.95
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:01.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7184.65
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:44.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.12
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.91e-3
p-value of test                       :    0.9981

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.43
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:03.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.67
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.22
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:32.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5095.93
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:55.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46092
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870092
  j =  1                              :        399907818
  j =  2                              :            46088
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46281
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870281
  j =  1                              :        399907442
  j =  2                              :            46273
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :  6.0e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    6.47
p-value of test                       :  6.1e-4    *****


-----------------------------------------------
CPU time used                    :  00:02:28.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-3
p-value of test                       :    0.9979

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.30
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:17.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:44.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.05e-3
p-value of test                       :    0.9932

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:58.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:55.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:37.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 9.13e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.16
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.46
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:38.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.46
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17411.51
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.65
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.02
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.45
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.76
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.10
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.12
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.08
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.95
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.13
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.94
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  424.20
p-value of test                       :    0.9939


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.79
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.63
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.56
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.36
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.93
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.22
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.43
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.37
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5127.85
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.94
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.20
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.73
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.56
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.66
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.30
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.62
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.81
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:22.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.05
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:22.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  6.8e-3

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.44e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.99e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.55e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 6.16e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.73
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.21
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.92e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.72
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:05.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:05.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9892.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.98
p-value of test                       :  9.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10399.74
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:52.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.26
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4933.25
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3953.71
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.31
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11937.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.87
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:29.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.77
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999862382

Normal statistic for number of bits   :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.43
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000019084

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.19
p-value of test                       :    0.9957

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.9e-3

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:26.02
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 46  MaxOft AD, t = 8                6.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 105644033.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1475
p-value of test                       :  1.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334595
  j =  1                              :        599997050
  j =  2                              :             1475
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5510
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:59.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4205
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:51.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:08.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:24.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:26.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:09.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:40.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:45.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    2.09
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:10.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:37.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.66
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.57
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.63
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.47
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.61
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:36.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1335.41
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:02.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6995.29
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:42.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.34
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:03.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.41
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.18
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:32.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5071.17
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:55.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46122
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870122
  j =  1                              :        399907764
  j =  2                              :            46106
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45513
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869513
  j =  1                              :        399908979
  j =  2                              :            45503
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.69
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:31.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:26.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.23e-3
p-value of test                       :    0.9954

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :  2.5e-3

Anderson-Darling statistic = A2       :    4.52
p-value of test                       :  5.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  1.6e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:10.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:36.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.95e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 3.38e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:35.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:35.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.66
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.47
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.77
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.94
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.68
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.99
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:05.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.29
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.71
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.60
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17273.38
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.88
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   58.50
p-value of test                       :  7.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.34
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.59
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.21
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.45
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.98
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.67
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.65
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.56
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.56
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.82
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.27
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.35
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.28
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.63
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.16
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.93
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.63
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4844.72
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.04
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.24
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.28
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.06
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4857.35
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  324.22
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.79
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:50.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.69
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:21.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.28
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:19.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 2.37e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.33e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.08
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.45
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.63
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:04.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.12
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:07.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.07
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.34
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:41.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.62
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.16
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.78
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12161.92
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11651.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:29.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.64
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999918302

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.71
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000053341

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.33e-4
p-value of test                       :    0.9994    *****

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -2.04
p-value of test                       :    0.98

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :  -0.049
p-value of test                       :    0.52

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:05.63

 All tests were passed




Server wird beendet - Lösche Semaphor 106692609.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5494
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:58.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:02.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:02.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:53.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:57.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:45.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    2.63
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     260
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    3.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:11.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:38.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.29
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.47
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.82
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.68
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.41
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.69
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.48
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  364.81
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.79
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:02.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7080.78
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:46.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.42
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:05.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.92
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.50
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5180.84
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:54.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45725
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869725
  j =  1                              :        399908557
  j =  2                              :            45711
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45952
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869952
  j =  1                              :        399908100
  j =  2                              :            45944
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:27.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:18.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9928

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.91e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.018
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.041
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:38.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:38.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.66
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.25
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.53
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.09
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.26
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.53
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.20
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.98
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17422.05
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.57
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.26
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.05
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.31
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.87
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.31
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.10
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.44
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.65
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.70
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.30
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.09
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.88
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.66
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.51
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.32
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.71
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.46
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.83
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.06
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.75
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  442.84
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.00
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  312.28
p-value of test                       :    0.9970


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.69
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.08
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  241.45
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.41
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:20.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.91
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.92e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.42e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.20
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.16
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.69
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:04.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:06.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10143.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10046.47
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:04:02.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:49.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.19
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4284.43
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4328.57
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11895.90
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:30.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.68
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000180406

Normal statistic for number of bits   :    1.43
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.40
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999923264

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9951

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.27

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:05.22

 All tests were passed




Server wird beendet - Lösche Semaphor 107741185.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:58.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7149
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:03.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7475
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:54.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:00.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    2.19
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:44.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     649
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:11.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:05.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.50
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:30.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.19
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.06
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.07
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.05
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.19
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  270.29
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.89
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7338.41
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.57
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:03.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.21
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.73
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5160.18
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:13.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45962
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869962
  j =  1                              :        399908080
  j =  2                              :            45954
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45818
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869818
  j =  1                              :        399908365
  j =  2                              :            45816
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:27.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:17.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.00e-3
p-value of test                       :    0.9990

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:45.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:59.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
p-value of test                       :    0.9912

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  8.6e-4    *****

Anderson-Darling statistic = A2       :    5.03
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:37.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 1.16e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:35.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.66
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:01:36.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.67
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.18
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.05
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.90
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.33
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.94
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17498.55
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.61
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.35
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.54
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.00
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.99
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.75
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.55
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.82
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.86
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.94
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.65
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.93
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.50
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.83
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.76
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.90
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.94
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.28
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.54
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.36
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.22
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.54
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.19
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.55
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.63
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.84
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.68
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.52
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.98
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.75
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:23.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.23
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:24.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.60
p-value of test                       :    0.9953

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 7.10e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.15e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.78
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.08
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:06.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.23
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:07.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9875.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10209.64
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : -6.89e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.081
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:39.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.35
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4750.07
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4257.61
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12140.77
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11890.54
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.24
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000154954

Normal statistic for number of bits   :    1.23
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.63
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000076366

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:00.62

 All tests were passed




Server wird beendet - Lösche Semaphor 108789761.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9931


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5404
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:00.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:43.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:59.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:00.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:06.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:04.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:56.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7482
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:01.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    3.16
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     964
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:12.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:42.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.08
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.45
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.38
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.50
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.46
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.39
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:05.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7055.80
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.90
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.65
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:08.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.15
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.53
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:37.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.30
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:00.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45730
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869730
  j =  1                              :        399908543
  j =  2                              :            45724
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45646
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869646
  j =  1                              :        399908710
  j =  2                              :            45642
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:29.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:37.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.02e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : 3.98e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:42.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   40.52
p-value of test                       :    0.9957

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.90
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.89
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.09
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.57
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.66
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.74
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17271.29
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.69
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.39
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.14
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.66
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.63
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.84
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.96
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.41
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.44
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.07
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.39
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.59
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.61
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.32
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.68
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.86
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.75
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.30
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.96
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.32
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.33
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.85
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5161.15
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.85
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.01
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.17
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.53
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.94
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.02
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.88
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.61
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -1.87
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:22.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.63
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:21.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.45e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 6.42e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.33e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.82
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.14
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.74
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:04.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.55
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:06.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.50
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.41
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:04:18.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:52.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4972.13
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:53.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.56
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3998.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11861.36
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11616.11
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:31.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.50
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999935807

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.66
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000084295

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:18.21

 All tests were passed




Server wird beendet - Lösche Semaphor 109740033.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:58.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:42.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:58.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:06.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:07.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:00.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:02.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:14.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.69
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:42.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.48
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.56
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.82
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.66
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.27
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.30
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.78
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.57
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7090.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:51.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.84
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.11
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.05
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:37.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5138.03
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:58.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45562
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869562
  j =  1                              :        399908879
  j =  2                              :            45556
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908145
  j =  2                              :            45923
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:30.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:20.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9932

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:07.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.92e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:42.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.062
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.32
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.25
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.38
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.46
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.91
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.17
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.70
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17799.48
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.69
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.75
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.97
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.40
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.98
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.29
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.06
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.17
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.81
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.99
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.93
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.38
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.31
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.30
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.46
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.85
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.42
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.14
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.08
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.73
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.82
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.91
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.46
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.79
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.96
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.49
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4878.67
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.88
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.95
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.74
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :    2.59
p-value of test                       :  4.8e-3



-----------------------------------------------
CPU time used                    :  00:02:25.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.10
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:26.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.92
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.65
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.07
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:05.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.92
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:06.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.60
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9894.87
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:04:21.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.56
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:52.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5014.19
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:55.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.06
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11691.52
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:31.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11895.84
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.46
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999875051

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.92
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000067879

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :  -0.095
p-value of test                       :    0.54

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:51.30

 All tests were passed




Server wird beendet - Lösche Semaphor 110854145.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:54.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4140
p-value of test                       :    0.9987


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:04.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:03.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:55.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:00.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.57
p-value of test                       :  4.7e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    2.02
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     641
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:14.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.90
p-value of test                       :  3.5e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    2.73
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:42.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.28
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.08
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.87
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.26
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  387.05
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.41
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6912.77
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:04.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.06
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   84.38
p-value of test                       :    0.9931


-----------------------------------------------
CPU time used                    :  00:01:32.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.66
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:59.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46057
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870057
  j =  1                              :        399907889
  j =  2                              :            46051
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45894
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869894
  j =  1                              :        399908217
  j =  2                              :            45884
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:27.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:18.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:54.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:33.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.51e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.65
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:01:33.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:34.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.31
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.50
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.03
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.52
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.16
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.38
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:37.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.90
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.96
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17435.13
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.21
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.60
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.13
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.51
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.26
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.19
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.92
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.58
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   45.48
p-value of test                       :  5.1e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.53
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.29
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.71
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  433.37
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.91
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.91
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.62
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.97
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.53
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.54
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.95
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.28
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.94
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4786.46
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.47
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.03
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.63
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.10
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.49
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.08
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.18
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:34.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.74
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:22.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.59
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:23.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.13

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.23e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.30e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 9.88e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.79
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.11
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.88
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:04.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 3.89e-3
p-value of test                       :    0.9960

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9863.18
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9869.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.034
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.055
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:42.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.18
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:49.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.35
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.82
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11947.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12139.94
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.43
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000081817

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.47
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999939662

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:58.38

 All tests were passed




Server wird beendet - Lösche Semaphor 112001025.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:56.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:05.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:54.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:59.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.65
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.60
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    3.79
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:12.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:44.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.88
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.93
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.30
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.75
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.82
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.79
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1407.86
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6953.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.07
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.63
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.69
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.19
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:32.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4971.35
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:58.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45888
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869888
  j =  1                              :        399908225
  j =  2                              :            45886
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46078
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870078
  j =  1                              :        399907845
  j =  2                              :            46076
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:27.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  5.1e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:18.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:56.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.63e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.70e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:34.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:34.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.38
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.00
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:48.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.99
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.77
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:38.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.12
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.78
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.72
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:39.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17658.26
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.35
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.87
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.57
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.75
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.60
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.32
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.02
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.51
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.82
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.16
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  400.45
p-value of test                       :    0.9996    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.27
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.02
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.29
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.99
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.34
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.15
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.01
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.77
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.96
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4897.50
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.54
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.88
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.27
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4859.56
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.92
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.00
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:34.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.53
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:20.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.08
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:19.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.17
p-value of test                       :    0.98

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 3.71e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.02
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.41
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.17
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:05.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9879.24
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.88
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:41.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.01
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5134.31
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.26
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11709.87
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:29.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.87
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000011101

Normal statistic for number of bits   :   0.088
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.40
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000111877

Normal statistic for number of bits   :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    3.00
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:42.57
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 J (L=1000, r=0)     0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 112951297.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:03.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:03.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5419
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:56.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4457
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:06.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:05.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:55.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:00.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    2.76
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.26
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:11.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.21
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.86
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.75
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.55
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.43
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.73
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.73
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:45.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.46
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:01.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7232.48
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.81
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.22
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:05.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.30
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.46
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4975.52
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:58.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45795
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869795
  j =  1                              :        399908414
  j =  2                              :            45787
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45814
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869814
  j =  1                              :        399908374
  j =  2                              :            45810
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:26.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:17.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:01.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:38.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.58e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.29e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 3.88e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.00
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.21
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.73
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.63
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:37.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.51
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.01
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17655.55
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.86
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.16
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.64
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.97
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.83
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.65
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.08
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.00
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.59
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.09
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.66
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.72
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.16
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.96
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.45
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  198.46
p-value of test                       :  2.5e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.70
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.53
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.23
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.64
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.80
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4899.03
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.25
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.77
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.03
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.17
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.14
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.97
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.84
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.46
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:20.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.36
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:21.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.15e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.48
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.16
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.71e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.06
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:04.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:05.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9889.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:42.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4996.23
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.96e-3
p-value of test                       :    0.9959

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5141.64
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:01:48.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.19
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.05
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11759.36
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11911.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.15
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999987308

Normal statistic for number of bits   :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.76
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000015454

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:53.10

 All tests were passed




Server wird beendet - Lösche Semaphor 113934337.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5349
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:57.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:07.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:07.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:57.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:01.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.36
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    2.20
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.95
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:14.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:43.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.68
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.19
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.19
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.20
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.74
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.13
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.87
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.05
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.21
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7067.20
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.28
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.94
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:03.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.42
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5214.62
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:58.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45918
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869918
  j =  1                              :        399908165
  j =  2                              :            45916
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45755
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869755
  j =  1                              :        399908495
  j =  2                              :            45745
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:27.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:17.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:00.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  1.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:55.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.5e-3

Anderson-Darling statistic = A2       :    4.14
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:33.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.01e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:34.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.96
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.05
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.93
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.15
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.30
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.48
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:39.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.85
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.95
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.89
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17259.09
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.70
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.76
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.12
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.57
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.80
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.25
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.67
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.42
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.44
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.02
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.60
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.53
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.66
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.67
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.81
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.44
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.18
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.06
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.01
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.48
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.43
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.59
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.80
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.76
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.43
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.17
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.64
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.13
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.38
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.54
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:21.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.66e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.98e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.22
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.22
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:04.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  255.89
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:02:04.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10098.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10078.29
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:39.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.23
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.88
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:49.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.65
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11626.69
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.85
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:29.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.28
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999956072

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.18
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000027385

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:30.95

 All tests were passed




Server wird beendet - Lösche Semaphor 114950145.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:50.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5235
p-value of test                       :    0.9943


-----------------------------------------------
CPU time used                    :  00:03:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:08.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:07.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:57.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:02.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.13
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:52.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    2.74
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     268
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:18.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:46.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.80
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.58
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.28
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.77
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.13
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.11
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7088.34
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.06
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:04.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.26
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.92
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:31.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4927.74
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:10.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45726
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869726
  j =  1                              :        399908556
  j =  2                              :            45710
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46062
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870062
  j =  1                              :        399907880
  j =  2                              :            46054
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:26.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:17.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:45.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9944

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:01.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:54.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:33.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 8.36e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:34.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.70
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.38
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.63
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.69
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.28
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17406.77
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.06
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.39
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.49
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.32
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.33
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.14
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.74
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.63
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.35
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.73
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.94
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.06
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.05
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.77
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.11
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.95
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.24
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.70
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.50
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.76
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.04
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.59
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.70
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5146.82
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.77
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.27
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.48
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.02
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.18e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.56e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.41
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.95
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:05.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.11
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:05.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10096.48
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10198.99
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.030
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:40.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.92
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.12
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.25
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4015.59
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12020.02
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12136.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.08
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999996170

Normal statistic for number of bits   :  -0.030
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.31
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999989243

Normal statistic for number of bits   :  -0.085
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.3e-3

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.23
p-value of test                       :    0.01

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.59
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.40
p-value of test                       :  8.1e-3

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:18.62

 All tests were passed




Server wird beendet - Lösche Semaphor 115965953.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1254
p-value of test                       :    0.9987

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334374
  j =  1                              :        599997492
  j =  2                              :             1254
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5442
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:59.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:58.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:08.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:08.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:56.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:03.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:52.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.18
p-value of test                       :  2.4e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.87
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    2.86
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:17.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:52.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.05
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.73
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.63
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.10
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.87
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.60
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:44.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:02.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7096.79
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:03.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.31
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.62
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5176.55
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:03.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46242
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870242
  j =  1                              :        399907521
  j =  2                              :            46232
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45741
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869741
  j =  1                              :        399908523
  j =  2                              :            45731
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.09e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9902


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:26.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:17.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.12
p-value of test                       :    0.9997    *****


-----------------------------------------------
CPU time used                    :  00:01:44.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:54.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 8.48e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:37.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.29
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:48.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.59
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.13
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.21
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.23
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.84
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.86
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17294.00
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.10
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.06
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    9.83
p-value of test                       :    0.9971


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.40
p-value of test                       :    0.9966


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.95
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.36
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.41
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.05
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.31
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.11
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.57
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.82
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.49
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.20
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.77
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.08
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.91
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.39
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.34
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.47
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.25
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.16
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.55
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.13
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.13
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.52
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5122.94
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.85
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.85
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:34.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.07
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:19.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.35
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:21.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 2.87e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.33e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 6.75e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.77
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.63
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.86
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:06.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.43
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:40.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.92
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.26
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3981.82
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.40
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.67
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11328.62
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.01
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999915221

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.71
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999949127

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.083
p-value of test                       :    0.53

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:09.48
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 48  MaxOft AD, t = 24               0.9997 
 100  HammingIndep, L=1200, r=25      0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 116981761.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5379
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:00.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:43.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7502
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:06.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:08.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:57.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:03.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:51.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.10
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.18
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    2.36
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    2.47
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:20.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:48.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.64
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.27
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.85
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.16
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.81
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.41
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.44
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.74
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1511.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:02.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7112.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.42
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.24
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:02.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.63
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.99
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:32.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4981.81
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:59.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45859
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869859
  j =  1                              :        399908283
  j =  2                              :            45857
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45695
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869695
  j =  1                              :        399908615
  j =  2                              :            45685
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:25.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:17.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:00.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:38.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.07e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.65e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:33.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.084
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:33.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.90
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.30
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.16
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.98
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.28
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.89
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.24
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.20
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.55
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.38
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.45
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17402.22
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.83
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.51
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.86
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.89
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.42
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.00
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.38
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.54
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.23
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.67
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.48
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  438.16
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.07
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.85
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.71
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.51
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.63
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.30
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.23
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.69
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.14
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.67
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.42
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.16
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.28
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.34
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.50
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.63
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.51
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:34.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.59
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -1.49
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:20.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.32
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -2.98
p-value of test                       :    0.9985



-----------------------------------------------
CPU time used                    :  00:02:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.75e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 3.02e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.43
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.84
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:04.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.03
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:05.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.68
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.07
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.092
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:04:07.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5023.17
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.7e-3

Kolmogorov-Smirnov- statistic = D-    : 1.07e-3
p-value of test                       :    0.9989

Anderson-Darling statistic = A2       :    4.50
p-value of test                       :  5.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4590.23
p-value of test                       :    0.9990

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.48
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.03
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11587.87
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.51
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.64
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999912398

Normal statistic for number of bits   :   -0.69
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.40
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999896936

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.018
p-value of test                       :    0.51

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:41.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.90e-3
p-value of test                       :    0.9904

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :  9.3e-4    *****

Anderson-Darling statistic = A2       :    6.08
p-value of test                       :  9.6e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :    3.24
p-value of test                       :  6.0e-4    *****

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  1.9e-3

Anderson-Darling statistic = A2       :    4.77
p-value of test                       :  3.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.79
p-value of test                       :  2.7e-3

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:02.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 105  AutoCor, d=1, r=27              6.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 117964801.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5431
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:00.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:06.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:07.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:00.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:04.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.70
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:51.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     335
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:18.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:50.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.97
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.67
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.83
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.78
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.08
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.37
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:44.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7047.36
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.55
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:03.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.25
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.65
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:32.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5160.55
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:57.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908164
  j =  2                              :            45915
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46068
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870068
  j =  1                              :        399907866
  j =  2                              :            46064
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:25.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:16.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:44.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:54.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:33.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 2.12e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.77e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.91e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.025
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.81
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.96
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.57
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.34
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.75
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.11
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.59
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17486.37
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.65
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.80
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.11
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.21
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.46
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.48
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.69
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.96
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.37
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.49
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.49
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.56
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.43
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.26
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.94
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.67
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  558.70
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.69
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.29
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.97
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.96
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5069.85
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.89
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.21
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.65
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.52
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.79
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  447.18
p-value of test                       :  8.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.26
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.74
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :   -1.68
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:21.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   31.11
p-value of test                       :  1.9e-3


-----------------------------------------------
Normal statistic for number of jumps  :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.86
p-value of test                       :    0.97

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 3.87e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.54e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 4.69e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.83
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.56
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   40.00
p-value of test                       :  4.5e-3



-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.02
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:03.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.61
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:04.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10203.04
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9815.92
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:43.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5108.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4996.76
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.51
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.97
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11786.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12067.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.53
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999959408

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.99
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999791000

Normal statistic for number of bits   :   -1.65
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.33
p-value of test                       :    0.9901

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:58.54

 All tests were passed




Server wird beendet - Lösche Semaphor 118980609.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:50.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1485
p-value of test                       :  6.5e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334605
  j =  1                              :        599997030
  j =  2                              :             1485
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:55.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:42.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:07.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:08.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:58.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:03.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     643
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    5.43
p-value of test                       :  1.8e-3

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.63
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    2.20
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:53.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.57
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.00
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.89
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.67
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:02.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7221.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.86
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.66
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:03.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.79
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.82
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:32.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5039.55
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:57.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45838
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869838
  j =  1                              :        399908327
  j =  2                              :            45832
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46166
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870166
  j =  1                              :        399907669
  j =  2                              :            46164
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:24.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:17.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:54.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.79e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 8.40e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.82
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.35
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.75
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.07
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.95
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.05
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.36
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.26
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17332.55
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.05
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.60
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.85
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.58
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.85
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.17
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.08
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   51.04
p-value of test                       :  1.0e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.93
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.73
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  197.52
p-value of test                       :  2.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.08
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.74
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.24
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.90
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  559.97
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.83
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.43
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.70
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.07
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.68
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.65
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  156.04
p-value of test                       :    0.9906


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.29
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.71
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.79
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.52
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.54
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   29.03
p-value of test                       :  3.9e-3


-----------------------------------------------
Normal statistic for number of jumps  :   -2.20
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:21.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.33
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:22.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.07
p-value of test                       :    0.02

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 8.68e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.46
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.98
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.51
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:03.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:04.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.11
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9859.21
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : 7.04e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4715.57
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.66e-3
p-value of test                       :    0.9940

Anderson-Darling statistic = A2       :    3.84
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4627.23
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.49
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11853.44
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11662.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.15
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000149008

Normal statistic for number of bits   :    1.18
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.76
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999961700

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.73
p-value of test                       :    0.04

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:27.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           6.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 119996417.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1487
p-value of test                       :  5.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334607
  j =  1                              :        599997026
  j =  2                              :             1487
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5371
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:59.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:43.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:59.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:09.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:08.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:01.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:05.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     948
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:52.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:17.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:49.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.94
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.50
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.50
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.11
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.54
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.49
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  278.77
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.88
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1538.53
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:03.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7012.56
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.50
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   39.82
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:03.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.20
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:34.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5003.86
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:53.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45820
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869820
  j =  1                              :        399908363
  j =  2                              :            45814
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45779
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869779
  j =  1                              :        399908442
  j =  2                              :            45779
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:25.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:18.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:45.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 4.57e-3
p-value of test                       :    0.9945

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.14e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:39.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.59
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.56
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.48
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.50
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.26
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17489.43
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.50
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.12
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.91
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.74
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.66
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.78
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.07
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.22
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.32
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.50
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.36
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.52
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.33
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.92
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.24
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.72
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.66
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.81
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.39
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.36
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.13
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.95
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.62
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.40
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.85
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.84
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.30
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.87
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.73
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.67
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   -1.91
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.32
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.12

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 5.48e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.90e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.18
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.72
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.23e-3
p-value of test                       :    0.9923

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.78
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:05.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.52
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9889.39
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.87
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:04:06.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4812.95
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.32
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:51.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.80
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12105.17
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11641.52
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.17
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000136306

Normal statistic for number of bits   :    1.08
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.40
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999862400

Normal statistic for number of bits   :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:31.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           5.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 121012225.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:36.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:34.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:52.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:01.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:00.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:53.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:56.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:10.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    3.19
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     181
p-value of test                       :  7.6e-3

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:35.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.80
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.33
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.52
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.32
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.86
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.55
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.50
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:05.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6859.67
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.77
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.01
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:07.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.25
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.48
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:38.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5030.76
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:00.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46104
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870104
  j =  1                              :        399907798
  j =  2                              :            46092
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45677
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869677
  j =  1                              :        399908654
  j =  2                              :            45661
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:29.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:17.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:59.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:52.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:32.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.84e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.37e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 3.14e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:41.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.77
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.56
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.37
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.60
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.12
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.84
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.65
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:46.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.99
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.18
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.13
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:29.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17312.27
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.06
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.91
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.12
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.69
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.12
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.43
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.50
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.38
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.23
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.53
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.05
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  591.63
p-value of test                       :  2.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.78
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.66
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.60
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.55
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.84
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.84
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.92
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.08
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.52
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.44
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.62
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.34
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:33.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.33
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.34
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5182.97
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.08
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.08
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:34.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.08
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:24.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.43
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:25.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.89
p-value of test                       :    0.97

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.14e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.30e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.54
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.36
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:07.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9958.24
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10058.83
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:04:15.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.92
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:51.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.89
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:52.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.41
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11926.13
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11811.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:31.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.19
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999952742

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.63
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  8000075928

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.82
p-value of test                       :    0.03

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-3
p-value of test                       :    0.9983

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.90
p-value of test                       :    0.03

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:14:39.14

 All tests were passed




Server wird beendet - Lösche Semaphor 101646338.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5412
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:50.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:39.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:08.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:09.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7165
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:07.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7161
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:12.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     944
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:17.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     182
p-value of test                       :  6.2e-3

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:42.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.30
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.90
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.51
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.72
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.30
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:59.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1513.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:09.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7122.47
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.61
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:14.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.35
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.65
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5058.10
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:13.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46253
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870253
  j =  1                              :        399907498
  j =  2                              :            46245
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45596
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869596
  j =  1                              :        399908809
  j =  2                              :            45594
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:28.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:19.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:11.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.68e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 9.07e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:50.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.28
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.02
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.75
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.40
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.29
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:04.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  165.53
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17191.87
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.65
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.89
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.65
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.26
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.65
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.97
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.74
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.20
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.29
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.61
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.88
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.07
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.79
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.52
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.64
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.57
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.15
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.59
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.44
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.88
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.32
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.36
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.17
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.87
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.92
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.65
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.47
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.37
p-value of test                       :    0.9923


-----------------------------------------------
Normal statistic for number of jumps  :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:26.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.53
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:26.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.73
p-value of test                       :    0.96

Sample variance                       :    1.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.11e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.50e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.91
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.56
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.53
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:06.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.01
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:06.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9805.80
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.58
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:04:37.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5019.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:52.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4740.48
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:54.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.40
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.47
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11974.70
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:33.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11734.56
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.76
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999848597

Normal statistic for number of bits   :   -1.20
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.82
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999940955

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:14:40.14

 All tests were passed




Server wird beendet - Lösche Semaphor 103153666.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:52.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:39.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:01.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:13.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:11.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:15.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     857
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:46.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.71
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:12.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:39.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.35
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.71
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.59
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.83
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.82
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.86
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.08
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1497.30
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:03.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6911.17
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.65
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.11
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:22.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.11
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.72
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4970.04
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:06.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45789
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869789
  j =  1                              :        399908423
  j =  2                              :            45787
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46225
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870225
  j =  1                              :        399907551
  j =  2                              :            46223
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:31.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.61e-3
p-value of test                       :    0.9920

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:08.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:38.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.21e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:51.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.63
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.00
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.27
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.72
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.20
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.62
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17012.63
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.80
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.35
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.44
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.72
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.61
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.93
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.98
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.12
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.78
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.38
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.14
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.22
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.92
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.09
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.73
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.06
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.48
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  311.50
p-value of test                       :    0.9973


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.56
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.22
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.29
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.55
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.31
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.09
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.33
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.35
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.86
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.21
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:25.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.39
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :    1.16
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:26.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.39e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.62
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.82
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.85
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.71
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:04.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9917.30
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:04:20.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4778.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3949.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11835.87
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11553.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:33.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.52
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999869045

Normal statistic for number of bits   :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.98
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999921464

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:34.65

 All tests were passed




Server wird beendet - Lösche Semaphor 104562690.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:48.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5562
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:55.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:07.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:06.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7490
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:59.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:04.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    2.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:14.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:43.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.26
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.09
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.89
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.30
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  264.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1361.80
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6962.12
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.31
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:07.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.11
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.92
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4976.07
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:51.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45940
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869940
  j =  1                              :        399908126
  j =  2                              :            45928
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45734
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869734
  j =  1                              :        399908536
  j =  2                              :            45726
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:29.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:18.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:02.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.24e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 5.48e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.014
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.47
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.35
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.93
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.56
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.68
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.56
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.62
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.95
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.23
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17410.25
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.50
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.42
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.80
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.88
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.94
p-value of test                       :    0.9936


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.58
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.26
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.52
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.49
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.57
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.92
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.94
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.03
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.93
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.52
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.57
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.45
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.34
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.38
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.46
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.82
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.00
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4872.98
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.75
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.36
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.70
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.31
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.68
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.10
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.85
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.58
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   -1.86
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:23.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.45
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -1.49e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 6.12e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.59e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 6.91e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.44
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.45
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.23
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:03.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.71
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:03.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10265.64
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10152.58
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:04:01.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.41
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4782.60
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.42
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.68
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11969.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.87
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999909044

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.03
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000001687

Normal statistic for number of bits   :   0.013
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :  -0.028
p-value of test                       :    0.51

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:08.39

 All tests were passed




Server wird beendet - Lösche Semaphor 105611266.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:48.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5445
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:55.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:40.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:05.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:06.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:55.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:04:02.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.30
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    3.98
p-value of test                       :  8.9e-3

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:16.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    2.40
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:46.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.78
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.80
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.90
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.81
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  281.97
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:44.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.77
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7022.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.76
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:05.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.25
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.01
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:32.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4933.58
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:53.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46184
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870184
  j =  1                              :        399907640
  j =  2                              :            46168
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908477
  j =  2                              :            45757
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:28.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:18.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:58.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:33.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 7.57e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 3.27e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.67
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   39.55
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.50
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.71
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.42
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.40
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17552.74
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.25
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.15
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.28
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.35
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.24
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.93
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.25
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.24
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.99
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.29
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.04
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.91
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.54
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.24
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.61
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.15
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.32
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.71
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.88
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.90
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.86
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.71
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.82
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.62
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.14
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.53
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.81
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  162.80
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.05
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:23.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.36
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :  -0.046
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.32
p-value of test                       :    0.99

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.55e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 8.15e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.05e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.80
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.12
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.34
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.26
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:05.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10084.30
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:35.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4996.20
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:44.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.03
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:44.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3978.36
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.97
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11507.49
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.38
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.74
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999979637

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.10
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999914912

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:36.57

 All tests were passed




Server wird beendet - Lösche Semaphor 106627074.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997171
  j =  2                              :             1413
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1242
p-value of test                       :    0.9996    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334362
  j =  1                              :        599997516
  j =  2                              :             1242
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1484
p-value of test                       :  7.2e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334604
  j =  1                              :        599997032
  j =  2                              :             1484
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:54.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:05.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7068
p-value of test                       :    0.9983


-----------------------------------------------
CPU time used                    :  00:03:07.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:01.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:02.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.88
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:16.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:45.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.14
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.61
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.94
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:05.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7113.53
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:05.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.23
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5057.70
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:54.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45964
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869964
  j =  1                              :        399908076
  j =  2                              :            45956
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46008
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870008
  j =  1                              :        399907987
  j =  2                              :            46002
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:28.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:18.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:45.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:56.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.29e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.022
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.77
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.10
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.25
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.84
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.92
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.38
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.93
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.50
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9943

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17764.32
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.65
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.51
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.19
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.27
p-value of test                       :    0.9934


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.77
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.08
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.15
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.57
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.50
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.66
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.37
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.84
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.52
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.26
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.58
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.16
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.79
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.72
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.95
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.72
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  310.87
p-value of test                       :    0.9975


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5094.92
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.60
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.44
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.26
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.65
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.84
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.98
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.78
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:34.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.73
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :   -2.22
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:22.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.17
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
p-value of test                       :    0.9939

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.95
p-value of test                       :    0.97

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.39e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.85
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.35
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:06.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:06.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.92
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.27
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:43.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.41
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.56
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4006.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3981.19
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11721.81
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.24
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.48
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000044056

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.36
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999921185

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:51.55
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9996 
 12  CollisionOver, t = 21           7.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 107642882.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:48.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997143
  j =  2                              :             1427
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5467
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:52.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:40.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4227
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7158
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:07.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:07.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:00.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:04:04.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    2.75
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     645
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:16.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:44.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.02
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.56
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.98
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.94
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:50.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1537.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7021.28
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.21
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:06.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.48
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.33
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:37.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4970.06
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:59.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45821
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869821
  j =  1                              :        399908360
  j =  2                              :            45817
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46358
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870358
  j =  1                              :        399907286
  j =  2                              :            46354
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:27.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:19.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:06.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:37.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 5.36e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.49
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.38
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.16
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.66
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:39.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17911.71
p-value of test                       :  5.2e-3



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.69
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.14
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.99
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.10
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.82
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.74
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.14
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.94
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.21
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.20
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.12
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.06
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.46
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.39
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.53
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.22
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.18
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.20
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.75
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5118.76
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.51
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.76
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.39
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.39
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.24
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  241.59
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.32
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:22.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.26
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :   -1.71
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:22.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :  2.9e-3

Kolmogorov-Smirnov- statistic = D-    : 5.43e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 6.32e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.54
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.04
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:04.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9930

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.87
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:04.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.90
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.91
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:59.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5071.75
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.68
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.11
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.08
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11752.81
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11712.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.89
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000096466

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.26
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000009598

Normal statistic for number of bits   :   0.076
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:28.60

 All tests were passed




Server wird beendet - Lösche Semaphor 108625922.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:53.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4242
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:05.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:05.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:56.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:01.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:15.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.84
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:43.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.86
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.10
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.54
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.88
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1356.35
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:02.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6944.12
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:44.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.66
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:05.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.79
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.69
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5102.60
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:54.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45793
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869793
  j =  1                              :        399908417
  j =  2                              :            45787
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45931
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869931
  j =  1                              :        399908142
  j =  2                              :            45923
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:27.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:17.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:34.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.15e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.75e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.67
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.58
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.81
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.04
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.46
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.13
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.77
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17182.24
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.91
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.14
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.67
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.98
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.01
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.14
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.98
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.18
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.07
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.20
p-value of test                       :  7.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.25
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.35
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.17
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.64
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.84
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.00
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.76
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.46
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.31
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.43
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  319.62
p-value of test                       :    0.9927


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5103.24
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.16
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  155.33
p-value of test                       :    0.9916


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.59
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.03
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.04
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.57
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.46
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.10
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:24.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.93
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    1.50
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9902

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.16
p-value of test                       :    0.98

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 8.79e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 3.48e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.98
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.35
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.43
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:06.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9958.87
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.83
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:34.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.02
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:47.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4198.02
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.86
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11768.01
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.34
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000142063

Normal statistic for number of bits   :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.87
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999979424

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:06.50

 All tests were passed




Server wird beendet - Lösche Semaphor 109608962.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:39.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:48.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1263
p-value of test                       :    0.9971

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334383
  j =  1                              :        599997474
  j =  2                              :             1263
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5326
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:53.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:06.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:56.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:04:01.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.34
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:14.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:45.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.01
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.16
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.01
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.37
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.11
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   25.80
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  273.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.05
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:42.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1494.86
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:01.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7115.93
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.99
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:06.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.11
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.10
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:33.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4952.92
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:59.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45667
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869667
  j =  1                              :        399908667
  j =  2                              :            45665
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45543
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869543
  j =  1                              :        399908920
  j =  2                              :            45531
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  4.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:28.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:45.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:56.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.21e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:38.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.43
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.38
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.63
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.14
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.41
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:44.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.18
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17437.50
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.24
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.06
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.98
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.12
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.35
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.80
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.62
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.90
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.32
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.93
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.63
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.19
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.26
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.73
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.05
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.11
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.83
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.84
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.42
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.83
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.31
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.52
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.19
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.78
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.16
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.57
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.03
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.24
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.12
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.18
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.24
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:23.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9986

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.29e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.94
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.48
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.51
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:09.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.21
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:07.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9805.29
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10102.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:36.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4752.94
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5028.58
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:50.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11712.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.10
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.87
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000028996

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.95
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999990794

Normal statistic for number of bits   :  -0.073
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :  -0.028
p-value of test                       :    0.51

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:08.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 33  CouponCollector, r = 27         0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 110592002.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:48.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:53.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:04.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:05.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:55.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:00.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    2.39
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     959
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    3.72
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9952


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    4.72
p-value of test                       :  3.9e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     250
p-value of test                       :    0.9983

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:16.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.94
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:44.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.34
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.98
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.41
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.24
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.23
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.14
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:43.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1441.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:02.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7048.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.04
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.80
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:04.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.14
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.35
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:32.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5097.19
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:58.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46243
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870243
  j =  1                              :        399907518
  j =  2                              :            46235
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46190
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870190
  j =  1                              :        399907624
  j =  2                              :            46182
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:28.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:19.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:33.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:37.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.26
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.74
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.80
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:48.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.31
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.65
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.00
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.84
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.81
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17799.29
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.72
p-value of test                       :  9.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.58
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.63
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.86
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.48
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.53
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.13
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.50
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.51
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.72
p-value of test                       :  6.8e-3


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.59
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.85
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.63
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.64
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.86
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.61
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.79
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.12
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.60
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.10
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4801.03
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.71
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.77
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.09
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.37
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.69
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.43
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.99
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.09
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :  -0.073
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.98
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.30e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.23e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.73
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.31
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.66
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.45
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:05.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
p-value of test                       :    0.9935

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9766.56
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.61e-3
p-value of test                       :    0.9918

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10318.23
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.98
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5046.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4226.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.97
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.51
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000041056

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.66
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000033526

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    0.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.1e-3

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.98
p-value of test                       :    0.02

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:57.20

 All tests were passed




Server wird beendet - Lösche Semaphor 111542274.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:54.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:57.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:05.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:05.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7485
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:57.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:03.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.27
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:13.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:43.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.39
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.83
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.82
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.77
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.09
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1366.91
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7218.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.35
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.02
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.18
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.76
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5030.40
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:59.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45888
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869888
  j =  1                              :        399908227
  j =  2                              :            45882
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46038
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870038
  j =  1                              :        399907928
  j =  2                              :            46030
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:27.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:19.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:35.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 6.13e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 5.15e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.42
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:37.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.085
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.70
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.07
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.95
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.29
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   46.86
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.68
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17311.56
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   60.74
p-value of test                       :  6.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   58.71
p-value of test                       :  7.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.87
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.54
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.16
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.45
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.06
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.64
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.39
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.75
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.40
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.22
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.39
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.65
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.32
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.79
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.89
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.70
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.81
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.56
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.53
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.02
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.65
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.69
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.25
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4888.93
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.52
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.46
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.44
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -1.56
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.40
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :  -0.024
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.91e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.26e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 8.67e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.35
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.01
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.64
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:05.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.03
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10060.29
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.39
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:37.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.51
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.64e-3
p-value of test                       :    0.9962

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4646.06
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.19
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4231.78
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12050.84
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11791.44
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.97
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000014071

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.54
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000143413

Normal statistic for number of bits   :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979

Tests on the sum of all N observations
Standardized normal statistic         :  -0.014
p-value of test                       :    0.51

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.17
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:48.56

 All tests were passed




Server wird beendet - Lösche Semaphor 112558082.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  4.0e-3


-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5309
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:51.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:40.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:39.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:55.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:01.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    2.59
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.07
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:13.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:43.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.48
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.33
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.57
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.80
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.19
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1381.46
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7142.51
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:41.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.53
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9906

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.90
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.67
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.85
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:32.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4916.45
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:59.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45930
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869930
  j =  1                              :        399908144
  j =  2                              :            45922
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45628
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869628
  j =  1                              :        399908747
  j =  2                              :            45622
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:28.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:19.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:01.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.50e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 9.71e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:37.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:38.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.93
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.11
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.53
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.49
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.30
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.00
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.09
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17497.87
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.70
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.75
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.04
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.11
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.10
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.12
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.10
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.78
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.27
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.90
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.43
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.93
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.92
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.59
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.60
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.60
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.03
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.82
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.71
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.66
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  459.76
p-value of test                       :  4.7e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.10
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.00
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.11
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.07
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.40
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.23
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.07
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.52
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.37
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -1.91
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:22.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.41
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:23.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.31e-3
p-value of test                       :    0.9966

Anderson-Darling statistic = A2       :    4.31
p-value of test                       :  6.5e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -3.02
p-value of test                       :    0.9987

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.34e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 3.64e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.49
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.52
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.70
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9793.86
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.13
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:39.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.75
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4775.53
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4250.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4287.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12075.32
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11597.59
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.62
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000131371

Normal statistic for number of bits   :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.13
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999974816

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.03
p-value of test                       :    0.98

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.52e-3
p-value of test                       :    0.9908

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.96
p-value of test                       :    0.03

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:54.73

 All tests were passed




Server wird beendet - Lösche Semaphor 113508354.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1264
p-value of test                       :    0.9968

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334384
  j =  1                              :        599997472
  j =  2                              :             1264
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:51.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:39.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:05.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7135
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:56.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:01.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    3.69
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:14.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.44
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.80
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.59
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.41
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.27
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.00
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.29
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:59.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7180.20
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.91
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.81e-3
p-value of test                       :    0.9939

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   39.72
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:02.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.47
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:48.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.63
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5130.25
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:59.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45506
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869506
  j =  1                              :        399908992
  j =  2                              :            45498
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45998
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869998
  j =  1                              :        399908009
  j =  2                              :            45988
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:27.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:17.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:01.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.91e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 4.55e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:41.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:40.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.93
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:48.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.96
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.70
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.08
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.75
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.98
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.84
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:37.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.40
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17360.00
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.85
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   57.80
p-value of test                       :  9.0e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.21
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.23
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.36
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.28
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.83
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.14
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.90
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.23
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.08
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.16
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  423.61
p-value of test                       :    0.9943


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.82
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.53
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.75
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.45
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.86
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.60
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.74
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.56
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.33
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.46
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.77
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.19
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.71
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.04
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5208.54
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.95
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.71
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.19
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:22.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.56
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.40e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.29
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.01
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.78
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.07
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:07.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9722.93
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10065.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:38.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.22
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3908.15
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.97
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11856.52
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11657.50
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.65
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999972047

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.73
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000029842

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:10.34

 All tests were passed




Server wird beendet - Lösche Semaphor 114458626.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5419
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:50.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:39.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:39.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:03.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7124
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:03.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:55.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:01.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.53
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:15.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.73
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.90
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.29
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.22
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.24
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.72
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.20
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:44.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6911.07
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.37
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   37.17
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:03:05.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.13
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.63
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:33.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5243.55
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:07.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45866
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869866
  j =  1                              :        399908272
  j =  2                              :            45858
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45766
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869766
  j =  1                              :        399908474
  j =  2                              :            45754
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:28.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:57.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9990

-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.84e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:35.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.26
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:47.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.20
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.75
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.34
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:48.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.29
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.44
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.06
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.11
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17432.15
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.49
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.78
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.63
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.16
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.39
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.80
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.39
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.58
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.77
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.16
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.94
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.38
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.90
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.24
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.67
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.45
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.09
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  608.78
p-value of test                       :  6.0e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.88
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.60
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.46
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.55
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5116.10
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.77
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.06
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.44
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.93
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.68
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.29
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.19
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.56
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.18
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   0.025
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -1.88
p-value of test                       :    0.97

Sample variance                       :    0.22
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.87e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.41
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.66
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.67
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:05.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9876.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10030.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:40.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4753.00
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.84
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4284.59
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.74
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11892.97
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11642.98
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   95.36
p-value of test                       :  4.4e-4    *****


-----------------------------------------------
Total number of bits:  8000169699

Normal statistic for number of bits   :    1.34
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.56
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000076651

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:45.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 J (L=1000, r=20)    6.0e-4
 101  Run of bits, r = 0              4.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 115376130.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:03.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:54.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4502
p-value of test                       :  6.4e-3


-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:03.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:56.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:01.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     939
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.10
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     329
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:12.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.92
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    2.38
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:39.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.85
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.71
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.45
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1326.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:00.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.37
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.52
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:03.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.53
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.40
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4961.78
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:07.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45785
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869785
  j =  1                              :        399908435
  j =  2                              :            45775
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46054
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870054
  j =  1                              :        399907894
  j =  2                              :            46050
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.56e-3
p-value of test                       :    0.9915

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:27.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:18.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 6.08e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:37.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:36.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.24
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.39
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:48.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.01
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.63
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.58
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:38.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.41
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.92
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17371.90
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.88
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.07
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.16
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.29
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.92
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.34
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.69
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.04
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.77
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.38
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.37
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.71
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.34
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.58
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.92
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.06
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.11
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.36
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  106.82
p-value of test                       :  7.5e-3


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.61
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.80
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.84
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.85
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.27
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.21
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.85
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4761.41
p-value of test                       :    0.9922


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.81
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.05
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :    1.69
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.59
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:22.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.84e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 9.94e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.81e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 6.56e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.70
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.85
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:03.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:04.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5072.74
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.40
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:51.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3925.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3997.78
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12020.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.66
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999869510

Normal statistic for number of bits   :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.65
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000100996

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    2.47
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:15.62

 All tests were passed




Server wird beendet - Lösche Semaphor 116326402.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:53.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4475
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:04.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:04.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:55.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:01.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.86
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    2.04
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.56
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9903

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:15.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    4.08
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:02:43.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.05
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.37
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.83
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.26
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.95
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.88
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1363.61
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:59.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7042.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:02.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.40
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.08
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4933.24
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:04.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46234
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870234
  j =  1                              :        399907536
  j =  2                              :            46226
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45710
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869710
  j =  1                              :        399908582
  j =  2                              :            45706
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:27.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:18.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:54.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    4.11
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.05e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.59e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.92e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:37.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.87
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.53
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.38
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.16
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.68
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.73
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.59
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.55
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.89
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17324.82
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.67
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.17
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.00
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.00
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.63
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.96
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.60
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.31
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.20
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.96
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.57
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.72
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.61
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.80
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.95
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.17
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  195.19
p-value of test                       :  4.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.62
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.02
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.72
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.16
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.49
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.60
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.43
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.37
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.37
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.44
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5143.99
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.47
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.14
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.70
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:22.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.80
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:21.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.74
p-value of test                       :    0.04

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.29e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.65e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.10
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.95
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:05.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.32
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:06.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9922.59
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10122.83
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:38.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.72
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.43
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.27
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11799.90
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.37
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.88
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000027094

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   31.44
p-value of test                       :    0.9940


-----------------------------------------------
Total number of bits:  8000025942

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9917

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    2.94
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:34.86

 All tests were passed




Server wird beendet - Lösche Semaphor 117374978.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5492
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:53.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4221
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:40.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4223
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:05.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:04.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7134
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:54.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:04:01.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.01
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    3.87
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:17.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:45.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.28
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.75
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.24
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.86
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.26
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.86
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.19
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.01
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  379.66
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:45.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.78
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6868.84
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.15
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:03.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.33
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.53
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5147.10
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:56.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45805
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869805
  j =  1                              :        399908395
  j =  2                              :            45795
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45368
p-value of test                       :    0.9916


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869368
  j =  1                              :        399909268
  j =  2                              :            45360
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:27.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:19.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:32.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.57e-5
p-value of test                       :    0.9901

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:37.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.17
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.07
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.35
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.62
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.58
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.76
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:38.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.98
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.20
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.29
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17618.87
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.02
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.52
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.75
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.40
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.25
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.56
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.43
p-value of test                       :    0.9906


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.17
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.64
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.18
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.56
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.61
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.33
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.30
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.19
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.57
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.15
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.11
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.90
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.12
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.45
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.44
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.57
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.23
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.41
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.53
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.68
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.98
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.15
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.01
p-value of test                       :  7.7e-3


-----------------------------------------------
Normal statistic for number of jumps  :    2.76
p-value of test                       :  2.9e-3



-----------------------------------------------
CPU time used                    :  00:02:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.14e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.11e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.58
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.02
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:59.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.57
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:03.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.50
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:05.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9888.22
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9958.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.097
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:38.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4776.87
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5054.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:50.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.45
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11574.90
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11732.98
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.34
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999953294

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   89.36
p-value of test                       :  1.8e-3


-----------------------------------------------
Total number of bits:  7999934451

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:08.47

 All tests were passed




Server wird beendet - Lösche Semaphor 118390786.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5364
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:56.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7163
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:04.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:55.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:01.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    2.08
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.40
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:14.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.16
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.69
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.06
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.92
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.90
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:44.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1487.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7051.62
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.14
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.65
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:04.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.96
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.33
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5119.74
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:57.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45923
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869923
  j =  1                              :        399908160
  j =  2                              :            45911
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46060
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870060
  j =  1                              :        399907882
  j =  2                              :            46056
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:26.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:20.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.50e-3
p-value of test                       :    0.9963

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:55.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.04e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:35.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.19
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.38
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.29
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.08
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.41
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.63
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.16
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   68.04
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.25
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17322.39
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.12
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.26
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.73
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.78
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.73
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.14
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.36
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.88
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.84
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.08
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.24
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.70
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.95
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.82
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.84
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.67
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.55
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.76
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.36
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.34
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5163.75
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  314.16
p-value of test                       :    0.9927


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.13
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.53
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.35
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.18
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.34
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.19
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.91
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:24.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.79
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.87e-3
p-value of test                       :    0.9960

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.79
p-value of test                       :    0.04

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.91e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 9.44e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 8.98e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.13
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.68
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:03.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.32
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10043.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9880.71
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:39.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4696.77
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4751.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11935.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11839.38
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.35
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000137935

Normal statistic for number of bits   :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.84
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999829559

Normal statistic for number of bits   :   -1.35
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:55.20

 All tests were passed




Server wird beendet - Lösche Semaphor 119373826.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:57.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:42.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:05.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:56.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:02.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    2.00
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:13.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:44.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.12
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.33
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.31
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.21
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.20
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.15
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.29
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.62
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.96
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:50.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.22
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:02.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6961.53
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:43.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.73
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.37
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.59
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4997.37
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:55.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45748
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869748
  j =  1                              :        399908507
  j =  2                              :            45742
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45762
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869762
  j =  1                              :        399908481
  j =  2                              :            45752
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  6.6e-3

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:26.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:18.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.79
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:01.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:32.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.81e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.085
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.013
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.057
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:33.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.75
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.82
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.25
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.85
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.51
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.66
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17506.15
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.60
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.38
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.25
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.88
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.80
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.48
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.18
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.02
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.87
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.89
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.07
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.38
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.15
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.61
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.85
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.58
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.90
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.25
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.41
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.99
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.17
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  431.02
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.94
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.23
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.45
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.63
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.19
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.38
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:34.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.40
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:22.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.46
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 7.82e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.75
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.61
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:04.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.44
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:04.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10251.29
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.61
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : 3.50e-4
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:36.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5032.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.69
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:50.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.25
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.55
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12215.58
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.54
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   84.82
p-value of test                       :  4.7e-3


-----------------------------------------------
Total number of bits:  7999908735

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.12
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000003448

Normal statistic for number of bits   :   0.027
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :  -0.073
p-value of test                       :    0.53

Sample variance                       :    2.29
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:54.02

 All tests were passed




Server wird beendet - Lösche Semaphor 120389634.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5409
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:56.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:06.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:05.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7093
p-value of test                       :    0.9959


-----------------------------------------------
CPU time used                    :  00:03:56.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:00.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.22
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    2.59
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:14.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.33
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    3.15
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     187
p-value of test                       :  2.0e-3

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:40.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.00
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.24
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.93
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.18
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.41
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.61
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.60
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:45.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.84
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6827.18
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:43.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.87
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.66
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:05.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.50
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.73
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5004.10
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:00.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46430
p-value of test                       :  5.2e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870430
  j =  1                              :        399907144
  j =  2                              :            46422
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45865
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869865
  j =  1                              :        399908277
  j =  2                              :            45851
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:27.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:19.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :  4.9e-4    *****

Anderson-Darling statistic = A2       :    5.50
p-value of test                       :  1.7e-3


-----------------------------------------------
CPU time used                    :  00:02:01.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:54.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.96e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:34.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:33.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.37
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.35
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.99
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.53
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.33
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.71
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.86
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.15
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17582.14
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.59
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.89
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.19
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   59.19
p-value of test                       :  8.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.65
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.73
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.42
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.83
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.96
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.43
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.76
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.04
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.85
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.26
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.30
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.53
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.63
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  444.49
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.09
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.27
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.98
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.17
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.80
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  468.10
p-value of test                       :  2.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5217.10
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.74
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  156.34
p-value of test                       :    0.9901


-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.54
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:19.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.14
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:20.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.05e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 4.83e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.14
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.35
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.06
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:02.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.57
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:02.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9661.64
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10281.69
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:25.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4793.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:39.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:38.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.69
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.85
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11839.73
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11765.86
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.95
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000014470

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.62
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000019888

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.94
p-value of test                       :    0.03

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   0.096
p-value of test                       :    0.46

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:00:09.55

 All tests were passed




Server wird beendet - Lösche Semaphor 121372674.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5616
p-value of test                       :  4.3e-3


-----------------------------------------------
CPU time used                    :  00:03:42.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:34.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:54.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:03.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:03.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:57.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:01.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.95
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    3.07
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     659
p-value of test                       :  9.2e-3

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    3.06
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:07.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.98
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:39.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.74
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.92
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.94
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.46
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.15
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.35
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.82
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.93
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  498.95
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:05.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7154.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.96
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.35
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:46.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   90.55
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:40.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4951.93
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:19.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46191
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870191
  j =  1                              :        399907618
  j =  2                              :            46191
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45931
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869931
  j =  1                              :        399908140
  j =  2                              :            45927
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:30.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9968


-----------------------------------------------
CPU time used                    :  00:02:17.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.07e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.34
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.79
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.31
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.69
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:50.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.91
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.40
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.22
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17603.09
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.56
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.46
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.11
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.47
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.09
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.13
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.18
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.84
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.96
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.94
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.24
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  205.28
p-value of test                       :  8.9e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  559.14
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.57
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.80
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.11
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.07
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  572.34
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.77
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.10
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.71
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.23
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.72
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.98
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.23
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.26
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.90
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4821.22
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.33
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  150.01
p-value of test                       :    0.9966


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.92
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:24.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.41
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:27.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.77e-3
p-value of test                       :    0.9939

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.70
p-value of test                       :  3.5e-3

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :-3.51e-17
p-value of test                       :    0.50

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.40e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.61
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.74
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.69
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:08.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.91
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:08.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.9e-3

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10215.04
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:04:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5113.89
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:53.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4773.35
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:55.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.18
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12011.02
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:34.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12038.98
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:33.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.73
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000093340

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.27
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999864026

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:17:19.30
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 M (L=1000, r=0)     8.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 101679107.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1248
p-value of test                       :    0.9993    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334368
  j =  1                              :        599997504
  j =  2                              :             1248
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5510
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:47.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:38.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:37.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:02.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:02.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:51.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:01.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    2.82
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:14.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:43.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.47
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.32
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  195.01
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.98
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.09
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:59.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7080.14
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.71
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:05.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.28
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.92
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5011.40
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:54.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45941
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869941
  j =  1                              :        399908121
  j =  2                              :            45935
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45874
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869874
  j =  1                              :        399908254
  j =  2                              :            45870
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:26.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:17.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:43.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:32.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 9.62e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : -2.42e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:31.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.94
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:47.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.86
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.62
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.69
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.65
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:42.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.54
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.60
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.07
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17554.16
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.85
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.17
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.42
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.02
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.70
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.62
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.74
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.06
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.52
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.94
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.80
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.20
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.15
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.36
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.83
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.65
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.25
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.37
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.78
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  455.81
p-value of test                       :  6.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.16
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.21
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.28
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  247.37
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.78
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.12
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.14
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.10
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.16
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.94
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:26.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.11
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 5.39e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.65e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 6.51e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.36
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.01
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:08.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    5.14
p-value of test                       :  2.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  145.23
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:02:08.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.19
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10124.66
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:40.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.14
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:47.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4784.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4013.56
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3995.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11666.26
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12066.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.24
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999912206

Normal statistic for number of bits   :   -0.69
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.36
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000012103

Normal statistic for number of bits   :   0.096
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.88

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:52.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  5  CollisionOver, t = 3            0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 103383043.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5549
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:48.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:38.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:36.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:03.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:02.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:52.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:01.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    2.88
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:13.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.52
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.34
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.83
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.56
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.13
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.79
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.61
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.83
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.03
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:59.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7141.00
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.57
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:03.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.87
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.70
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:35.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5116.87
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:00.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45968
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869968
  j =  1                              :        399908069
  j =  2                              :            45958
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46056
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870056
  j =  1                              :        399907893
  j =  2                              :            46046
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:27.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:17.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:33.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.29e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 4.65e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.061
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:32.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:32.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.09
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.34
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.38
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.94
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.20
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17517.20
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   67.78
p-value of test                       :  1.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.06
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.46
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.86
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.69
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.72
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.61
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.82
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.32
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.45
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.37
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.96
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  563.67
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.29
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.71
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.79
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.42
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.25
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.99
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.54
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.28
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.42
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5200.57
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.67
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.99
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  320.41
p-value of test                       :    0.9920


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.45
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.27
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.31
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.20
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.90
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :    1.19
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:25.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.73
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:25.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 9.38e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.48
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.32
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.88e-3
p-value of test                       :    0.9938

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:08.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:07.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9748.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9707.73
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:44.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.27
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.24
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3981.04
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.06
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11880.77
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12269.12
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.76
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999989396

Normal statistic for number of bits   :  -0.084
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.75
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999955160

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:27.96

 All tests were passed




Server wird beendet - Lösche Semaphor 104235011.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5296
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:47.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:38.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:37.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:01.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:01.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:52.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:00.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     639
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:13.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.31
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    2.29
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    2.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:45.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.52
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.41
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.90
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.74
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.02
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.46
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1561.95
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6987.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:42.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.98
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.91
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:03.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.77
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.26
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:34.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4961.57
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:55.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908184
  j =  2                              :            45905
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45678
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869678
  j =  1                              :        399908647
  j =  2                              :            45672
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:26.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  7.1e-3

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:16.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 9.63e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.057
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.073
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:39.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:39.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.37
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:48.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.97
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.47
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.09
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.42
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.08
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.66
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.0e-3

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.24
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.59
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17366.94
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.45
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.64
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.21
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.59
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.88
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.39
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.58
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.00
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.31
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.84
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.01
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.49
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.14
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.56
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.43
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.87
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  179.59
p-value of test                       :  7.3e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.11
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.60
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.16
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.80
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.92
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.26
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.31
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.74
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.50
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.43
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.49
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -1.53
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:25.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.10
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.10e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.95e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.25
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.53
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:07.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  244.86
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:07.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9827.02
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:42.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.50
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.68
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.81
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11680.99
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11659.95
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.68
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000027241

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.47
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000054151

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.057
p-value of test                       :    0.48

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:41.98

 All tests were passed




Server wird beendet - Lösche Semaphor 105218051.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5528
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:48.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:38.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:37.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:02.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:01.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:53.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:00.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.63
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:16.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.23
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.15
p-value of test                       :    0.9982

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:46.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.62
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.79
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.92
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.15
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.34
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.59
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1498.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:59.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6814.37
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:01.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.94
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.62
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:34.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5139.81
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:59.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45674
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869674
  j =  1                              :        399908653
  j =  2                              :            45672
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46297
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870297
  j =  1                              :        399907413
  j =  2                              :            46283
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:27.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:17.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.76
p-value of test                       :  3.8e-3


-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 9.76e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.56
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.071
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:34.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.22
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.23
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:47.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.58
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.21
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.83
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.05
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.74
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.69
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17622.37
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.42
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.66
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.08
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.01
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.67
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.73
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.85
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.50
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.23
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.23
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.84
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.63
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.86
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.29
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.85
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.11
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.90
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.74
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.37
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.41
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.52
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.15
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.54
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.87
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.88
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.08
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.46
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.35
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.39
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    2.11
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.36
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.11e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.76e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.92
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.63
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.19
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:08.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.66
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:07.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.06
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9831.62
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:42.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4961.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4753.77
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:50.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.67
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3970.16
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11862.14
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.37
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000000388

Normal statistic for number of bits   : 3.07e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.81
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999976877

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -2.03
p-value of test                       :    0.98

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:45.20

 All tests were passed




Server wird beendet - Lösche Semaphor 106102787.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5416
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:47.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:38.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:38.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:03.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:01.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:52.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:57.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:12.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:39.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.60
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.70
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.22
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.47
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.80
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.04
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:42.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:04.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6956.93
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:45.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.81e-3
p-value of test                       :    0.9982

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   38.63
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:03.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.05
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.11
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5262.89
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:55.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45732
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869732
  j =  1                              :        399908542
  j =  2                              :            45720
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45943
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869943
  j =  1                              :        399908120
  j =  2                              :            45931
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:28.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:18.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:59.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:32.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.28e-5
p-value of test                       :    0.9935

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 5.35e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   98.97
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:00:46.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.95
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.18
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.83
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.43
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.01
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.16
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17383.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.60
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.08
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.13
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.46
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.20
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.86
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.44
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.57
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.92
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.99
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.44
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.64
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.27
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   46.68
p-value of test                       :    0.9946


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.32
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.35
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.12
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.75
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.36
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.02
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.49
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.10
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  246.95
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.63
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.65
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.14
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.82
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.28
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    2.16
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:24.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.33
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:23.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 5.88e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.44e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.09
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.35
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.08
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:04.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.33
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:06.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9931

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.77
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.076
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:50.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5064.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.22
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:51.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.36
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.55
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.39
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11436.59
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.40
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999944594

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.28
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999939341

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:08.70

 All tests were passed




Server wird beendet - Lösche Semaphor 107053059.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5379
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:50.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4210
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:38.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4444
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:02.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:01.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:52.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:59.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:17.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:45.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.73
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.04
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.24
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.75
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.46
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.80
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.33
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1367.04
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:04.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.00
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.76
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.34
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:04.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.43
p-value of test                       :    0.9943


-----------------------------------------------
CPU time used                    :  00:00:46.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.75
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:36.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5038.01
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:58.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45968
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869968
  j =  1                              :        399908067
  j =  2                              :            45962
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45475
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869475
  j =  1                              :        399909054
  j =  2                              :            45467
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  7.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:28.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:17.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:59.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:32.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 7.27e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.71e-4
p-value of test                       :  4.0e-3

Kolmogorov-Smirnov- statistic = D-    : 5.01e-6
p-value of test                       :    0.9990

Anderson-Darling statistic = A2       :    4.38
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:38.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.63
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.34
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.72
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.40
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.57
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.15
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.94
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17297.47
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.54
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.49
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.34
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.18
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.78
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.57
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.46
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.25
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.25
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.49
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.59
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.47
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.15
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.90
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.17
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.40
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.55
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.81
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.55
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.24
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.53
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.25
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.65
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.28
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.05
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.73
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.50
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.83
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :   -1.30
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:20.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.99
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:20.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    2.52
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.78e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.77e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.06
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.60
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:06.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:08.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10173.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10186.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:04:04.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.31
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4991.43
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:50.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.68
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12017.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11754.08
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.66
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000168811

Normal statistic for number of bits   :    1.33
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.21
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000175120

Normal statistic for number of bits   :    1.38
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:05.27

 All tests were passed




Server wird beendet - Lösche Semaphor 108003331.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5295
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:49.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:39.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:39.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:03.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:53.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:59.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.91
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:16.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:39.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.72
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.31
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.86
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.16
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.34
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.34
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:02.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6969.45
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.42
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:03.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.40
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.71
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:32.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5102.46
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:57.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45798
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869798
  j =  1                              :        399908407
  j =  2                              :            45792
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45989
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869989
  j =  1                              :        399908024
  j =  2                              :            45985
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:28.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:18.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.69
p-value of test                       :  3.6e-3

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.075
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.12
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.27
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.04
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.92
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.94
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:40.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.20
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.81
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.62
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17290.48
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.51
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.57
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.45
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.98
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.42
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.17
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.14
p-value of test                       :    0.9963


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.82
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.17
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.22
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.98
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.16
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.62
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.35
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.46
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.50
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.07
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.19
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.28
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.79
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5131.44
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.64
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.05
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.66
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.97
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4885.91
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.55
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.86
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.01
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:22.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.80
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :   -1.69
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:24.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :1.40e-16
p-value of test                       :    0.50

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.22e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.72
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.97
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.87
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:07.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.79
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:08.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10220.44
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10114.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:39.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4745.65
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.06
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3910.10
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11941.38
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:29.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.80
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000034603

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.67
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000020002

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:57.61

 All tests were passed




Server wird beendet - Lösche Semaphor 108986371.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:51.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:38.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:03.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:53.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:59.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.27
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    2.79
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:17.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:43.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.41
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.60
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.78
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.69
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.54
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.07
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.71
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  367.05
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1441.21
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:00.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7037.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.51e-3
p-value of test                       :    0.9944

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   50.87
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.41
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:04.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.93
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.14
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5046.26
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:10.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45752
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869752
  j =  1                              :        399908499
  j =  2                              :            45746
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46170
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870170
  j =  1                              :        399907664
  j =  2                              :            46162
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:17.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:28.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:18.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:45.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.90e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:34.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.15
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.73
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.81
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.37
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17620.86
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.34
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.71
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.77
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.47
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.45
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.89
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.29
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.58
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.12
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.14
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.15
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.77
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.54
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.71
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.91
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.68
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  209.18
p-value of test                       :  4.7e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.75
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.60
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  103.89
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.87
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.81
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.93
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.42
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.32
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.80
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.53
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.80
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.22
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.35
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.53
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -1.76
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.88
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :  -0.082
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:23.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.94e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.41
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.78
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.53
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:04.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:05.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9872.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10241.88
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:42.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4992.51
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4716.68
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.07
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11823.15
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12083.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.91
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999961745

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.24
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999935339

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:05.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 M (L=1000, r=20)    4.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 109936643.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5306
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:54.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:39.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:57.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:06.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:58.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:01.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:51.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    2.35
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    4.46
p-value of test                       :  5.3e-3

Stat. AD after spacings (mNP2-S)      :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:16.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    3.21
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:45.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.61
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.25
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.32
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.05
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.30
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.15
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:05.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7106.45
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.55
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.28
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:10.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.82
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.30
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5056.58
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:59.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45678
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869678
  j =  1                              :        399908650
  j =  2                              :            45666
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45927
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869927
  j =  1                              :        399908150
  j =  2                              :            45919
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    4.30
p-value of test                       :  6.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  4.3e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:30.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 2.88e-3
p-value of test                       :    0.9969

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  5.0e-3

Anderson-Darling statistic = A2       :    6.14
p-value of test                       :  8.7e-4    *****


-----------------------------------------------
CPU time used                    :  00:02:19.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:05.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.29e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.03
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.90
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.74
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.20
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.13
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.02
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17258.76
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.59
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.15
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.09
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.64
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.25
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.60
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.07
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.26
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.77
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.41
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.25
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.98
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.44
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.93
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.93
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.54
p-value of test                       :    0.9952


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.49
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.17
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.37
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.70
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.83
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.28
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.58
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.69
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.18
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.62
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.90
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.99
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:34.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.77
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -0.98
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:21.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.50
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :    2.01
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:21.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.77e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 8.91e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.60
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.71
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:07.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.47
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:07.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9828.83
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9931.40
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:04:20.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  6.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4670.65
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:52.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5038.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3946.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11735.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11767.94
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.67
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999930875

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.04
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000033535

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :  -0.040
p-value of test                       :    0.52

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:34.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 47  MaxOft AD, t = 16               8.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 110919683.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5426
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4456
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:08.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:06.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:02.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:05.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    2.78
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:15.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    2.03
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:41.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.72
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.78
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.56
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.14
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.64
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.69
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.56
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:53.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.14
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:06.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7144.48
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:57.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.25
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:14.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.78
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.74
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4948.03
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:57.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45726
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869726
  j =  1                              :        399908553
  j =  2                              :            45716
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45754
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869754
  j =  1                              :        399908494
  j =  2                              :            45750
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:30.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:17.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  5.4e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:03.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:57.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 8.63e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.55e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.034
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:44.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.65
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.66
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.13
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:51.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.95
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.85
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.11
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17493.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.02
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.94
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.50
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.59
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.55
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.91
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.45
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.18
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  188.97
p-value of test                       :  9.6e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.93
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.83
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.50
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.42
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.84
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.00
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.22
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.40
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.00
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.50
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.51
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.70
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.68
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.69
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.54
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.62
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.04
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  267.34
p-value of test                       :  1.0e-3


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.94
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:23.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.25
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :   -1.48
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:24.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.06e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 8.55e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.04
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.94
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:05.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.23
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:05.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9908.95
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9839.66
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.086
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:04:26.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:54.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.86
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4377.67
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11715.93
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:33.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11696.94
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:34.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.28
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999885092

Normal statistic for number of bits   :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.97
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999988772

Normal statistic for number of bits   :  -0.089
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:48.40

 All tests were passed




Server wird beendet - Lösche Semaphor 112033795.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5544
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:53.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4453
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:39.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4447
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7085
p-value of test                       :    0.9969


-----------------------------------------------
CPU time used                    :  00:03:05.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7100
p-value of test                       :    0.9947


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:00.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9955

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:12.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.53
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.92
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.27
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.55
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.85
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.08
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.34
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:06.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7098.97
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.62
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.66
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:18.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.38
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.71
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:36.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5034.62
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:57.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908373
  j =  2                              :            45806
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46239
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870239
  j =  1                              :        399907527
  j =  2                              :            46229
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:29.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:01.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.92e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 3.53e-4
p-value of test                       :  6.9e-3

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.032
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:40.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.84
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.10
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:55.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.03
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.83
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.23
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.69
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.99
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.31
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17347.22
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.47
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.39
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.99
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.61
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.43
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.13
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.34
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.80
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.95
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.20
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.68
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.12
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.05
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.70
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.76
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.26
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.38
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.24
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.61
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4866.47
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.32
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.79
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.70
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.73
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4862.23
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.03
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.36
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.51
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:23.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.07
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:24.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.67e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.79
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.25
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.12
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:08.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.82
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:09.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9814.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.62
p-value of test                       :    0.9957

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.087
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:04:10.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.55
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:53.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.93
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11652.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12124.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:31.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.61
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999971537

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.90
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999972839

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:23.53

 All tests were passed




Server wird beendet - Lösche Semaphor 113180675.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:54.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:10.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:08.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:05.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:09.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.70
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:14.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.99
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:40.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.01
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.09
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.22
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.58
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.01
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  384.98
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:57.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.49
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:08.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7100.94
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:20.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.18
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:47.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.01
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5009.65
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:00.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46246
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870246
  j =  1                              :        399907511
  j =  2                              :            46240
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46003
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870003
  j =  1                              :        399907996
  j =  2                              :            45999
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:32.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.45e-3
p-value of test                       :    0.9908

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  6.4e-3

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  8.2e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:21.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:53.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:10.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:57.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:39.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.13e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:24.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:44.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.27
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.96
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.07
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.69
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.26
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:51.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.33
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.05
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17784.64
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.48
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.90
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.35
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.72
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.07
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.04
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.78
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.81
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.37
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.91
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.23
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  437.53
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.59
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.67
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.30
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.50
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.38
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.37
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.80
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.53
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.43
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5120.43
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.40
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.49
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.68
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.75
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5095.51
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.24
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.16
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.01
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:24.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.35
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    1.82
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.41e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.03
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.68
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.06
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:03.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.35
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:04.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.37e-3
p-value of test                       :    0.9944

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10290.86
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.93
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:04:31.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.76
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:56.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.16
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:59.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.82
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.15
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11683.82
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11955.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.96
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999839501

Normal statistic for number of bits   :   -1.27
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.84
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000059710

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.12e-3
p-value of test                       :    0.9989

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.59
p-value of test                       :    0.9951

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.99
p-value of test                       :    0.02

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:57.14

 All tests were passed




Server wird beendet - Lösche Semaphor 114262019.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1477
p-value of test                       :  1.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334597
  j =  1                              :        599997046
  j =  2                              :             1477
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5409
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:50.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:39.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7137
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:38.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:03.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:04.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:55.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:02.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     953
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:13.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.90
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.84
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.89
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.03
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.72
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  371.59
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1545.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7066.30
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:41.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.78
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.15
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:04.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.64
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.67
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4982.59
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:08.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45416
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869416
  j =  1                              :        399909172
  j =  2                              :            45408
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45512
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869512
  j =  1                              :        399908976
  j =  2                              :            45512
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:28.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:18.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:58.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 4.80e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:38.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:37.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.26
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:47.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.03
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.67
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:47.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.61
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:37.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9950

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.28
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.89
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17027.57
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.53
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.76
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.21
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.96
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.13
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.32
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.22
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.18
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.08
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.42
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.52
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.98
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.72
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.28
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.23
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.62
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.64
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.40
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.02
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.85
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5160.72
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.26
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.77
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.89
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.90
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4867.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.37
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.39
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.56
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.37
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    1.43
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:24.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :  -0.060
p-value of test                       :    0.52

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.44
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.67
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.20
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:07.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.33
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:06.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10055.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.1e-3

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10244.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:40.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.30
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.44
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.50
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11697.71
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11670.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.26
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999951011

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.49
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999878312

Normal statistic for number of bits   :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9987

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.042
p-value of test                       :    0.52

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:09.87

 All tests were passed




Server wird beendet - Lösche Semaphor 115408899.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5312
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:55.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:04.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:03.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:00.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     943
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    3.72
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:53.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.22
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.08
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:16.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:43.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.84
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.21
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   27.91
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.08
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.04
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  181.34
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1375.99
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7001.49
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.59
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.63
p-value of test                       :    0.9917

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.67
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:04.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.85
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:46.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.69
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4947.68
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:08.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45960
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869960
  j =  1                              :        399908085
  j =  2                              :            45950
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45828
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869828
  j =  1                              :        399908353
  j =  2                              :            45810
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:27.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:18.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:58.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:33.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.36e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.58
p-value of test                       :  4.9e-3

-----------------------------------------------
CPU time used                    :  00:01:40.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.83
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.45
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.99
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.74
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.82
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.25
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:39.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.05
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   15.28
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17124.33
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:52.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.50
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.88
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.60
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.04
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.66
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.15
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.72
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.82
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.40
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.67
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.86
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.05
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.50
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.23
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.99
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.66
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.65
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.11
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.25
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.12
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.47
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.01
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.83
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.58
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.30
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.31
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.46
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.62
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.34
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.62
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.28
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    1.66
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:23.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.96
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -0.98
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.53e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.96e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 6.74e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.80
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.33
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.26
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:03.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.89
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:04.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10165.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9912.73
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.058
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.098
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:54.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4755.38
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.48
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:51.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.67
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.11
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11547.97
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:29.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.25
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000153481

Normal statistic for number of bits   :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.33
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999932321

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.30e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.82
p-value of test                       :    0.03

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:51.68

 All tests were passed




Server wird beendet - Lösche Semaphor 116359171.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:40.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:54.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:41.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7527
p-value of test                       :  7.7e-3


-----------------------------------------------
CPU time used                    :  00:03:05.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:55.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7472
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:03.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:51.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:15.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.10
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.52
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.42
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.08
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.86
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.16
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.75
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.69
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.45
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6921.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:42.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.27
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.41
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:04.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.05
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.42
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:34.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5072.32
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:12.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45752
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869752
  j =  1                              :        399908500
  j =  2                              :            45744
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45651
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869651
  j =  1                              :        399908706
  j =  2                              :            45635
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:27.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:18.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.53e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.045
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.86
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.33
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  111.60
p-value of test                       :  5.1e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.20
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.09
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.26
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.98
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.50
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17539.69
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.59
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.55
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.84
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.19
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.79
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.12
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.03
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.41
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.30
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.08
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.28
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.47
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.12
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.54
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.58
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.93
p-value of test                       :    0.9936


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.10
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.82
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.07
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.48
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.81
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.48
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.56
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.79
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.30
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.15
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.22
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.25
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.34
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.82
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.36
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -1.38
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.35
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:21.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.2e-3

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.06
p-value of test                       :    0.02

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.81e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 6.42e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.53
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   44.00
p-value of test                       :  2.8e-4    *****



-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.69
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.17
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:04.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.79
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9847.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.14
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:40.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:51.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3964.76
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11672.07
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11862.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:29.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.68
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999912956

Normal statistic for number of bits   :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.23
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999928670

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    2.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9940

Tests on the sum of all N observations
Standardized normal statistic         :  -0.074
p-value of test                       :    0.53

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:04.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 61  WeightDistrib, r = 28           5.1e-4
 86  LongestHeadRun, r = 0           2.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 117342211.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5536
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:55.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:59.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:07.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:06.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:00.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:06.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.04
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    2.67
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     837
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.42
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:15.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:44.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.12
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.60
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.58
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  518.78
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:05.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6759.42
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.02
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:09.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.92
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.29
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4954.96
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:17.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46008
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870008
  j =  1                              :        399907986
  j =  2                              :            46004
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45795
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869795
  j =  1                              :        399908413
  j =  2                              :            45789
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:29.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
p-value of test                       :    0.9926

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:18.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:02.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:56.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.75e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.83
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.89
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.36
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    4.08
p-value of test                       :  8.3e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.95
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.65
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.59
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17171.69
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.88
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.72
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.43
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.92
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.13
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.82
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.56
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.88
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.85
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.06
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.60
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.33
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.32
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.92
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.78
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.83
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.12
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.42
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.59
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.97
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.14
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.23
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.88
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.95
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.04
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.27
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.02
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.98
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.67
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :  -0.091
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:21.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.55
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -1.49
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:21.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.74e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 8.36e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.35
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.84
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 9.64e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.92
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:06.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.62
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:06.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10078.29
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.36
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:04:16.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:51.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9901

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.77
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:52.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3992.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12018.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.07
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999997277

Normal statistic for number of bits   :  -0.022
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.33
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999865658

Normal statistic for number of bits   :   -1.06
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    2.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:33.86

 All tests were passed




Server wird beendet - Lösche Semaphor 118456323.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:54.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:40.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:04.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:05.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:56.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:00.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    3.01
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.49
p-value of test                       :  5.2e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.84
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:12.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.58
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.86
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.66
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.79
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.89
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.96
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  495.71
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.81
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7072.84
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.36
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:02.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.15
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.01
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5028.71
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:03.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45817
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869817
  j =  1                              :        399908369
  j =  2                              :            45811
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45660
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869660
  j =  1                              :        399908683
  j =  2                              :            45654
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:28.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.84e-3
p-value of test                       :    0.9947

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:46.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:00.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 8.28e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.055
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -9.59e-4
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.25
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.38
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.34
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.69
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.36
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.79
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.39
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.03
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.69
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17623.87
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.54
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.81
p-value of test                       :    0.9930


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.05
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.58
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.20
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.57
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   45.25
p-value of test                       :  7.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   46.15
p-value of test                       :  4.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.45
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.67
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.67
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.02
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.07
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.03
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.38
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.27
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.53
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  101.29
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.57
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.53
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.19
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.97
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.04
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.02
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.59
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.45
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.53
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.99
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.36
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:34.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.89
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:21.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.91
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    1.74
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:22.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.19
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.73
p-value of test                       :    0.04

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.95
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.36
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.96
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:03.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.10
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:05.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9950.68
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10277.39
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.070
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:38.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.64
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4958.66
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.23
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4276.05
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11911.59
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12117.73
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.28
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000055381

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.35
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000047332

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :  6.9e-4    *****

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    4.65
p-value of test                       :  4.5e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.39
p-value of test                       :    0.9917

Sample variance                       :    0.15
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:03.42

 All tests were passed




Server wird beendet - Lösche Semaphor 119439363.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:55.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:04.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:06.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:56.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    2.78
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     648
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    4.80
p-value of test                       :  3.6e-3

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:13.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.91
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:40.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.52
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.05
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.17
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.69
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.21
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.74
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.38
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:45.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1401.01
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:00.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6984.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:40.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.85
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:02.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.41
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.36
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5037.50
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:04.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45779
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869779
  j =  1                              :        399908444
  j =  2                              :            45775
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45564
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869564
  j =  1                              :        399908878
  j =  2                              :            45552
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:27.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:17.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:45.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:34.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.20e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:39.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:40.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.87
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.08
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.20
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.93
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   48.23
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-3
p-value of test                       :    0.9988

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   66.89
p-value of test                       :  4.9e-3

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.14
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.80
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17412.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.80
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.71
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.09
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.21
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.77
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.47
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.75
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.48
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.86
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.29
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.26
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  573.75
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.18
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.63
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.28
p-value of test                       :    0.9916


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.45
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.52
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.73
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.09
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.89
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.71
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.05
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.76
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.44
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.86
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.40
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.11
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.92
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.94
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.31
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :    2.07
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:23.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.75
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.58e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.03
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.66
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:02.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.46
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:03.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10094.76
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9987.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:42.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.29
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.41
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:51.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.85
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.93
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11591.65
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11831.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.45
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999992927

Normal statistic for number of bits   :  -0.056
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.44
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999931007

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -2.00
p-value of test                       :    0.98

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:57.55

 All tests were passed




Server wird beendet - Lösche Semaphor 120455171.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997327
  j =  2                              :             1335
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5555
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:54.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7161
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:55.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:01.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    2.78
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     855
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:12.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:38.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.09
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.38
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.98
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.33
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.99
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.28
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:45.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1560.97
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:00.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7095.62
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:41.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.56
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:02.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.21
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.69
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5040.69
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:00.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45682
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869682
  j =  1                              :        399908638
  j =  2                              :            45678
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46004
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870004
  j =  1                              :        399907995
  j =  2                              :            45998
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9921

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:27.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:18.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 3.94e-3
p-value of test                       :    0.9958

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.85e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.065
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:38.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:37.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.70
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.31
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.85
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.57
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.71
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:38.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.34
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.20
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.30e-3
p-value of test                       :    0.9955

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.21
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 9.33e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16944.21
p-value of test                       :    0.9956



-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.06
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.24
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.51
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.34
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.38
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.37
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.11
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.87
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.23
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.46
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.67
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.96
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.83
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.07
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.15
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.04
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.93
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.49
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.33
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.10
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.01
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.50
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.40
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.30
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5082.84
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.05
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.18
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.13
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:19.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.94
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:19.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.88
p-value of test                       :    0.97

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 7.68e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 4.82e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.50
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.74
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9917.06
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10130.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:24.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.78
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:40.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.76
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:36.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.20
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11934.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11880.30
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:10.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.79
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000062920

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.04
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999978026

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:58:42.45

 All tests were passed




Server wird beendet - Lösche Semaphor 121470979.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:42.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:34.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:55.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:01.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7562
p-value of test                       :  2.3e-3


-----------------------------------------------
CPU time used                    :  00:03:01.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:54.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:59.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    3.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     640
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.37
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:12.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.63
p-value of test                       :  4.8e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:36.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.61
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.28
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.79
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.10
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.88
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.26
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  387.42
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1343.92
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6898.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.07
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.77
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:02.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.82
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.08
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:35.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4998.93
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45941
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869941
  j =  1                              :        399908123
  j =  2                              :            45931
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45610
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869610
  j =  1                              :        399908787
  j =  2                              :            45596
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:29.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:18.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.95e-3
p-value of test                       :    0.9933

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:52.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 5.50e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.059
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:34.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.54
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.37
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.23
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.17
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.98
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.21
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.29
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.47
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.34
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17388.54
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.81
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.94
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.38
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.56
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.39
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.30
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.99
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.01
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.55
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.17
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:40.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.93
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.74
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.70
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.03
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.74
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:47.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.51
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.29
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.71
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.94
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.79
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.78
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.93
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.14
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.03
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.48
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.60
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.05
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.53
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.16
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.03
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.53
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   0.079
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:21.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.25
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:16.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    2.52
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.84e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 8.33e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.89e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.06
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.27
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.84
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:07.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.60e-3
p-value of test                       :    0.9919

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.89
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:10.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10124.21
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9794.12
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:43.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.85
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4814.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4296.59
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.95
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11675.40
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11540.64
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.53
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999990611

Normal statistic for number of bits   :  -0.074
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.87
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999945422

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   0.015
p-value of test                       :    0.49

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:39.06

 All tests were passed




Server wird beendet - Lösche Semaphor 101711876.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1463
p-value of test                       :  4.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334583
  j =  1                              :        599997074
  j =  2                              :             1463
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:43.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:36.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:35.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:54.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7143
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:00.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:01.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:52.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:57.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    2.65
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:12.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.96
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.61
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.92
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.25
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.18
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.03
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.55
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:00.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6906.83
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:45.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:03.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.52
p-value of test                       :    0.9913


-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.74
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5082.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:08.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46271
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870271
  j =  1                              :        399907462
  j =  2                              :            46263
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46257
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870257
  j =  1                              :        399907488
  j =  2                              :            46253
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:29.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:53.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 6.16e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:35.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.00
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:48.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.07
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.97
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.04
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.21
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.73
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:43.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.08
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.08
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.44
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17383.49
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.82
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.23
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.54
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.08
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.78
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.46
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.77
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.74
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.06
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.67
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.06
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.94
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.97
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.77
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.92
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.86
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.10
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.84
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.09
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.95
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.42
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.68
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.28
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.71
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.59
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.92
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.30
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.49
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.02
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.57
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.12
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:21.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.90
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :    1.38
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:19.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.49e-3
p-value of test                       :    0.9942

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.9e-3

Anderson-Darling statistic = A2       :    5.51
p-value of test                       :  1.8e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.26
p-value of test                       :  5.6e-4    *****

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.91
p-value of test                       :    0.03

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:11.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.51e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 6.74e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.34e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.66e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.08
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.00
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:09.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.51
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:09.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10166.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:56.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.49
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.26
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.35
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11674.71
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.82
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:29.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.84
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000132361

Normal statistic for number of bits   :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.75
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000064549

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:54.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 82  LempelZiv, r = 0                5.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 102825988.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5290
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:46.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:37.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:35.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:54.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:01.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:01.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:53.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:57.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:11.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.63
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.31
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.52
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.41
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.72
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.77
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.92
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.04
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.77
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1386.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:58.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7053.20
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:44.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.47
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:03.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.67
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.24
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:34.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5121.03
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:05.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45916
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869916
  j =  1                              :        399908174
  j =  2                              :            45904
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45982
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869982
  j =  1                              :        399908037
  j =  2                              :            45980
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:28.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:54.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:33.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 5.32e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 9.91e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:34.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:34.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.48
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.22
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.16
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:47.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.01
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.07
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.14
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17429.14
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.51
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.17
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.78
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.81
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.26
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.54
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.68
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.41
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.56
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.65
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.98
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.24
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.88
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.61
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.02
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.61
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.00
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.04
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.42
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.32
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.91
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.36
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.75
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.67
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.81
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.98
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.79
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.15
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.28
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:34.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.07
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:19.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.08
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :   0.025
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:19.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.54e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.59e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.61e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.16
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.51
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:07.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.68
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:07.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.64
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.40
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:50.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4739.64
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.23
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.83
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.88
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11935.63
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11942.18
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:30.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.03
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999802883

Normal statistic for number of bits   :   -1.56
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.79
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999943949

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.93
p-value of test                       :    0.03

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.93
p-value of test                       :    0.03

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:33.05

 All tests were passed




Server wird beendet - Lösche Semaphor 103841796.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5367
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:49.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:35.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:54.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7503
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:01.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:03.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:54.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:55.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.01
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:10.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.49
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:33.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.74
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.90
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.98
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.21
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.47
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.83
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.37
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:06.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6975.63
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.74
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:09.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.69
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.43
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:37.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5033.81
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:13.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45836
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869836
  j =  1                              :        399908332
  j =  2                              :            45828
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45470
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869470
  j =  1                              :        399909062
  j =  2                              :            45466
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:30.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:18.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:01.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.61e-4
p-value of test                       :  5.5e-3

Kolmogorov-Smirnov- statistic = D-    : 4.23e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.83
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 8.34e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:44.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.89
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.71
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.98
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.36
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.34
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.58
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:39.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17403.09
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.76
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.60
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.25
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.08
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.18
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.36
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.59
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.40
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.70
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.52
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.88
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.81
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.53
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.71
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.08
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.07
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.74
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.46
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.77
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.34
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.42
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.27
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5129.18
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.49
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.72
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.30
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.51
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.21
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.57
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.91
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.60
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:21.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.33
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:23.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 5.71e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.92e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 9.57e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.53
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.56
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:06.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  156.94
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9971.79
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.1e-3

Anderson-Darling statistic = A2       :    4.11
p-value of test                       :  8.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10382.99
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:04:18.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.90e-3
p-value of test                       :    0.9915

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5114.41
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:52.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.52
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:54.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.71
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.39
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11717.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:31.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11525.67
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:32.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.19
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000141814

Normal statistic for number of bits   :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.81
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999983219

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.23
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:42.77

 All tests were passed




Server wird beendet - Lösche Semaphor 104890372.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:48.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:38.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:37.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4464
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:55.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7137
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:03.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:02.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:51.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7485
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:57.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.54
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    2.23
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     546
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:12.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:42.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.28
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.45
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.02
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.94
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.32
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.09
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:58.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6933.65
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.36
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:02.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.50
p-value of test                       :    0.9920


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.70
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4948.62
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:07.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45795
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869795
  j =  1                              :        399908413
  j =  2                              :            45789
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45704
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869704
  j =  1                              :        399908595
  j =  2                              :            45698
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:28.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:17.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:45.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 9.19e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.95
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.33e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.49e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:35.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:33.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.01
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.92
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.54
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.26
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:47.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.24
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.01
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.35
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17516.80
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.02
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.72
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.31
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.04
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.90
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.90
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.20
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   44.40
p-value of test                       :  3.0e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.01
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.57
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.82
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.20
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.47
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.70
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.42
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.13
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.97
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  457.67
p-value of test                       :  5.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.91
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.33
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.18
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.31
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.07
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.39
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.79
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.65
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.73
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:34.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.39
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:23.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.14
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    1.26
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:23.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.17e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 8.99e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.11
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.18
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.51
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:07.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.57
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:09.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9971.73
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.50
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:39.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.70
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:51.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11804.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11966.38
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.95
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999981584

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.61
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000078106

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:55.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 C (L=50, r=25)      3.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 105971716.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:16.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5352
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:48.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:38.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:06.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:53.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:00.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9913


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    2.54
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:13.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:42.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.29
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.38
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.25
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.88
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.88
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.65
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.52
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.83
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1486.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:04.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7036.79
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.08
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:11.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.13
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.87
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:37.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5209.93
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:04.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46094
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870094
  j =  1                              :        399907818
  j =  2                              :            46082
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45860
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869860
  j =  1                              :        399908284
  j =  2                              :            45852
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:31.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:06.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9962

-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:36.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 3.92e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.67
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.42
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.42
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.03
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.60
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:39.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17257.29
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:52.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.13
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.18
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.79
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.25
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.61
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.28
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.97
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.15
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.27
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.28
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.08
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.04
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.15
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.51
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.85
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.16
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.51
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.31
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.88
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.18
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.01
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.44
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4759.12
p-value of test                       :    0.9927


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.50
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.78
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.93
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.11
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.21
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.50
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.00
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.21
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    2.08
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:26.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.89
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -0.79
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:26.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :  -0.022
p-value of test                       :    0.51

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 8.82e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.86e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.66
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   23.93
p-value of test                       :  2.4e-3

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9967

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.26
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:07.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.12
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:07.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9694.64
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.66
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:04:25.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.62
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:54.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5042.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:56.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3996.91
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11801.28
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11793.25
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.97
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999922799

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.48
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999944918

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:31.71

 All tests were passed




Server wird beendet - Lösche Semaphor 106987524.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5480
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:50.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:38.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:38.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:54.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:01.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:54.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:59.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9917


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:11.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    5.36
p-value of test                       :  2.0e-3

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:42.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.38
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.66
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.01
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.22
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.86
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  280.56
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:43.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6998.51
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.86
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.48
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:03.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.78
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:34.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4946.34
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:03.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45750
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869750
  j =  1                              :        399908503
  j =  2                              :            45744
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46034
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870034
  j =  1                              :        399907933
  j =  2                              :            46032
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:28.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:01.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:54.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:31.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.87e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.12e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:35.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.089
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:37.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.70
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.86
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.12
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:47.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.84
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.23
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.23
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.21
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.47
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.60
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17345.24
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.34
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.13
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.90
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.65
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.60
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.73
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.54
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.89
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.36
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.89
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.27
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.98
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.19
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.06
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.00
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.42
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  564.30
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.90
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.38
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.99
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.49
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.86
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.36
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.93
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.73
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.90
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4847.23
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.40
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.12
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.69
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:26.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.68
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:24.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.19e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 6.59e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.63
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.76
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:05.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.68
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:04.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.22
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:46.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4757.90
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.89
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.44
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4293.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11930.64
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11648.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.01
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999997991

Normal statistic for number of bits   :  -0.016
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.65
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000075172

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.15

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:14.43

 All tests were passed




Server wird beendet - Lösche Semaphor 108134404.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5212
p-value of test                       :    0.9978


-----------------------------------------------
CPU time used                    :  00:03:51.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:57.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:04.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:59.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    2.08
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:12.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:42.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.15
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.89
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.06
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.40
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.33
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.69
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.83
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.10
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.72
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:06.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7147.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.33
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.65
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:09.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.11
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.61
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5087.47
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:59.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45794
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869794
  j =  1                              :        399908420
  j =  2                              :            45778
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45533
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869533
  j =  1                              :        399908936
  j =  2                              :            45529
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:30.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:18.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.52e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.68e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.98
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.09
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   62.29
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.69
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.70
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17132.20
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.12
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.91
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.76
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.61
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.44
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.70
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.35
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.17
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.40
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.15
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.95
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.36
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.61
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.40
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.00
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  433.98
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.47
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.17
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.98
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.79
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.84
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.02
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.53
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.62
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.74
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.90
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.77
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.87
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:24.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.09
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:25.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.34e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.56e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.85
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.73
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.15
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:05.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.6e-3

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:06.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10128.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10181.74
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:04:19.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.44
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:52.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:53.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4209.14
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4271.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11957.50
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:31.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11799.43
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:32.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.83
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999879833

Normal statistic for number of bits   :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.55
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000086125

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    0.46
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:27.35

 All tests were passed




Server wird beendet - Lösche Semaphor 109117444.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:51.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1239
p-value of test                       :    0.9997    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334359
  j =  1                              :        599997522
  j =  2                              :             1239
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5455
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:53.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:55.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:57.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:04.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:05.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:57.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7174
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:00.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.16
p-value of test                       :    0.9980

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:12.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:41.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.55
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.18
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.97
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.66
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:05.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7072.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.07
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.90
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:09.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.73
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.79
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:37.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5102.40
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:58.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46313
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870313
  j =  1                              :        399907375
  j =  2                              :            46311
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46238
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870238
  j =  1                              :        399907526
  j =  2                              :            46234
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:29.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  6.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:17.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 9.91e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:43.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.82
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.90
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.73
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.34
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.71
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.48
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17485.70
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.86
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.51
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.23
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.74
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.03
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.59
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.65
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.27
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.08
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.70
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.08
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.66
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.88
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.47
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.33
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.70
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.27
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.46
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.35
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.66
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.95
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.66
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.40
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.63
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.08
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.94
p-value of test                       :    0.9959


-----------------------------------------------
Normal statistic for number of jumps  :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:25.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.69
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:23.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.41e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.28e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.00
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.27
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.74
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:05.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9868.39
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10128.60
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:04:16.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4742.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:53.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.22
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4010.99
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4250.37
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11910.81
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:31.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.57
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:30.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.80
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999942626

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.76
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999993752

Normal statistic for number of bits   :  -0.049
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.76
p-value of test                       :    0.04

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:45.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 110231556.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:52.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:39.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:03.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:54.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:00.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:12.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.99
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.00
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.98
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.59
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.34
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.58
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1355.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:02.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7207.18
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:42.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.24
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.71
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:03.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.13
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.38
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5147.36
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:55.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46102
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870102
  j =  1                              :        399907799
  j =  2                              :            46096
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45950
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869950
  j =  1                              :        399908101
  j =  2                              :            45948
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:27.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:01.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:54.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:32.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.12e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.14e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.055
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.59
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.12
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.73
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.72
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.17
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.88
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.87
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17640.97
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.14
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.11
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.15
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.70
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.77
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.04
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.69
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.50
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.47
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.93
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.36
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.75
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.56
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.36
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.62
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.00
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.84
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.08
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.05
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.79
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.96
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.78
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.79
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  249.00
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.74
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.63
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.27
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.22
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.86
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.10
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:22.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.09
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.27e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 6.12e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.43
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.64
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.99
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:07.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.26
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:07.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9839.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9934.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -3.06
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:03:40.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.13
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.48
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.42
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.40
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11614.01
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.64
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.56
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999964436

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.96
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999991703

Normal statistic for number of bits   :  -0.066
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         : 2.48e-3
p-value of test                       :    0.50

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:51.69

 All tests were passed




Server wird beendet - Lösche Semaphor 111378436.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:39.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1250
p-value of test                       :    0.9991    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334370
  j =  1                              :        599997500
  j =  2                              :             1250
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1470
p-value of test                       :  2.4e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334590
  j =  1                              :        599997060
  j =  2                              :             1470
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5458
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:52.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4452
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:10.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:08.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:05.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:07.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    2.59
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     663
p-value of test                       :  5.9e-3

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.97
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     271
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:14.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:38.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.19
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.10
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.13
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  294.98
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.31
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.97
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:05.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7050.19
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.04
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.16
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:18.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.92
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:46.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.36
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:41.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5047.46
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:01.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45730
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869730
  j =  1                              :        399908543
  j =  2                              :            45724
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45966
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869966
  j =  1                              :        399908070
  j =  2                              :            45962
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:31.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:20.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:52.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:08.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:56.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:39.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 6.85e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9990

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 3.79e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.19
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.05
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.85
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.34
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:11.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.87
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.79
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.95
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17315.94
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.01
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.85
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.57
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.32
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.51
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.48
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.21
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.49
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.07
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.24
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.38
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.24
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.49
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.33
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.25
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.61
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.55
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.04
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.71
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.20
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.90
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.94
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.95
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.40
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.21
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.02
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.42
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.74
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.39
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:24.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.57
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -1.29
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:23.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 5.74e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.98
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.76
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:04.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.39
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:05.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9890.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10111.45
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:04:26.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.90
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4755.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:58.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.29
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.44
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:34.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11944.60
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:35.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.44
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000023533

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.99
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999949208

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.02
p-value of test                       :    0.98

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:18.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  6  CollisionOver, t = 3            0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 112295940.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5369
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:53.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:06.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:59.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:03.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.26
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:13.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:42.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.92
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.48
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.52
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.74
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:03.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6991.60
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.05
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.40
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:08.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.89
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.97
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:37.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4949.31
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:02.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45945
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869945
  j =  1                              :        399908111
  j =  2                              :            45943
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45424
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869424
  j =  1                              :        399909154
  j =  2                              :            45420
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:30.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:02.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.51e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.59e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 3.56e-4
p-value of test                       :  6.3e-3

Anderson-Darling statistic = A2       :    3.75
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.061
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.88
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.22
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.92
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.69
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.41
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.20
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.11
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.82
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17444.04
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.33
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.87
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.89
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.07
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.41
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.84
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.86
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.00
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.86
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.97
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.19
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.76
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.04
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.83
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.81
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.75
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.10
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.56
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.40
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.04
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.03
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.90
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.59
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.79
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.29
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.67
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.58
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  323.02
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.03
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.06
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:24.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.56
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:23.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.50e-3
p-value of test                       :    0.9953

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.35
p-value of test                       :    0.9907

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.30e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9925

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.24e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 4.66e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.98
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.21
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:03.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.96
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:05.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9822.43
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10126.15
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:04:15.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.60e-3
p-value of test                       :    0.9930

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4677.31
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:52.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5097.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:53.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4243.54
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.41
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11535.57
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12040.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.60
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999917132

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.30
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999927047

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.09

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.97

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:04.29

 All tests were passed




Server wird beendet - Lösche Semaphor 113410052.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:51.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5360
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:52.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:39.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:05.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:06.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7471
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:00.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:03.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:47.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.17
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:13.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    2.35
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.99
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.45
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.80
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.55
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.59
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.53
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.85
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:50.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1373.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:04.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7243.36
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.67
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:09.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.85
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.93
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4999.92
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:04.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908072
  j =  2                              :            45955
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46321
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870321
  j =  1                              :        399907362
  j =  2                              :            46313
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:30.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:18.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:03.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:55.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:36.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.87e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 3.65e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.080
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.02
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.22
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.36
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:39.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 3.86e-3
p-value of test                       :    0.9960

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17833.30
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.68
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.27
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.16
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.40
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.63
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.98
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.19
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.64
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.68
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.19
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.18
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  439.73
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.47
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.64
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.25
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.03
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.64
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.17
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.39
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.05
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.28
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.70
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.38
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  147.04
p-value of test                       :    0.9981


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.25
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.68
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4800.04
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.81
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.36
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.46
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.78
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    1.40
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:21.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.70e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.74
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.76
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.86
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:05.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:05.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9902.17
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.68
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:04:15.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.33
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:52.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.75
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:52.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3991.93
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3985.13
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.38
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:30.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.25
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:30.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.25
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999810026

Normal statistic for number of bits   :   -1.50
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.84
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000013717

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :  -0.060
p-value of test                       :    0.52

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:33.62

 All tests were passed




Server wird beendet - Lösche Semaphor 114491396.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5507
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:53.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:42.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:59.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7486
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:12.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:10.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:14.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:13.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.06
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.57
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.76
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.36
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.19
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.01
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:09.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7176.23
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:58.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.45
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.77
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:17.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.27
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:47.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.72
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5116.14
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:01.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45768
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869768
  j =  1                              :        399908468
  j =  2                              :            45760
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45783
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869783
  j =  1                              :        399908439
  j =  2                              :            45773
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:32.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:21.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:53.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:11.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:38.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 7.64e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 9.03e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:24.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:50.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:54.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.78
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.34
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.32
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.01
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.09
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.64
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.23
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17533.68
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.78
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.35
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.50
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.57
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.58
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.17
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.79
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.16
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.41
p-value of test                       :    0.9900


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.46
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.17
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.50
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.62
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.58
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.94
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.15
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.13
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.28
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.75
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.27
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.75
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.40
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.82
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.06
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.03
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.19
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.59
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.18
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    0.51
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:22.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.01
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :    1.53
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:21.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 2.17e-3
p-value of test                       :    0.9978

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.26e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.98
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.31
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.93
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:03.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:04.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9959.87
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9857.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:04:25.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.06
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.95
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:00.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3988.73
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3871.41
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11599.97
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:37.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11853.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.79
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999992729

Normal statistic for number of bits   :  -0.057
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.39
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999834689

Normal statistic for number of bits   :   -1.31
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:45.73

 All tests were passed




Server wird beendet - Lösche Semaphor 115572740.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5392
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:55.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:42.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:07.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7490
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:07.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:59.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:04.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.20
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    4.06
p-value of test                       :  8.2e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     961
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    2.94
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:15.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.55
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:42.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.39
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.59
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.22
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.18
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.58
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.44
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.79
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.89
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:07.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6962.38
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:51.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.20
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.85
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:11.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.98
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.97
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:37.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5104.19
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:01.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45927
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869927
  j =  1                              :        399908150
  j =  2                              :            45919
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46146
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870146
  j =  1                              :        399907711
  j =  2                              :            46140
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:30.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:20.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:04.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:37.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 3.06e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:51.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.34
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.16
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.35
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.75
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.64
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.97
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.98
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.36
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17353.07
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.85
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.13
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.88
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.59
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.74
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.45
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.89
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.26
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.19
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.14
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.23
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.77
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.87
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.81
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.46
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.99
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.70
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.02
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.47
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.47
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.06
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.97
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.53
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.20
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.52
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.07
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.60
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.41
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.84
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :    1.75
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:20.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.02
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:19.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.12
p-value of test                       :    0.02

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.35e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 5.59e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.45e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 7.96e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.34
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.37
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:05.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:05.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9664.09
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9870.20
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:04:10.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.13
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:52.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4814.54
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:52.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4253.70
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4204.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11923.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11440.23
p-value of test                       :    0.9942

-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.62
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000058069

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.15
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999970988

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:03.61

 All tests were passed




Server wird beendet - Lösche Semaphor 116686852.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5338
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:54.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:41.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:07.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:07.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7131
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:04:00.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:05.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.17
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:16.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:44.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.47
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.36
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.45
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.26
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.11
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.59
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.19
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.57
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.32
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:03.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7024.41
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:49.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.53
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:08.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.45
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   76.41
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5174.66
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:00.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45341
p-value of test                       :    0.9941


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869341
  j =  1                              :        399909320
  j =  2                              :            45337
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45727
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869727
  j =  1                              :        399908550
  j =  2                              :            45719
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  6.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.95
p-value of test                       :  9.3e-3


-----------------------------------------------
CPU time used                    :  00:02:30.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:06.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:36.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.50e-4
p-value of test                       :  7.5e-3

Kolmogorov-Smirnov- statistic = D-    : 6.45e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.68
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 7.40e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.97
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.98
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.99
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.65
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.67
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.57
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.87
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.78
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17560.30
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.17
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.98
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.66
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.64
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   44.03
p-value of test                       :  3.4e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.29
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.52
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.25
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.71
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.79
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.61
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.45
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.91
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.69
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  103.75
p-value of test                       :    0.9968


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.78
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.49
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.29
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.07
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.26
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.27
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.80
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.54
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:34.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.95
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.39
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.19
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.09
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.95
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   0.083
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:21.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.15
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -1.20
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:21.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   0.000
p-value of test                       :    0.50

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    2.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 9.14e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 3.50e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.80
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.84
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.62
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:04.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.34
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:04.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9842.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9801.54
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:04:08.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.48
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5001.35
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:52.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11883.87
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11898.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.90
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000129130

Normal statistic for number of bits   :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.86
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000039001

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:41.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 41  Permutation, t = 5              0.9991 
 74  RandomWalk1 C (L=50, r=0)       3.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 117702660.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:40.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5274
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:55.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:41.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:07.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:07.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:02.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:05.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9923

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:15.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:44.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.37
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.54
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.18
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.84
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.32
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.48
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.42
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:04.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7130.35
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:51.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.53
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:09.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.71
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.73
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:37.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5072.33
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:00.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45858
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869858
  j =  1                              :        399908287
  j =  2                              :            45852
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46135
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870135
  j =  1                              :        399907735
  j =  2                              :            46125
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:30.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:19.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:51.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:03.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.10e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.073
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 9.98e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.52
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.68
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.14
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.14
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.55
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.64
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.59
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.08
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.76
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17241.20
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.77
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.89
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.82
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.88
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.99
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.83
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.35
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   46.88
p-value of test                       :  5.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.39
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.06
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.42
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.69
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.18
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.75
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.11
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.79
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.85
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.92
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.40
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.29
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.88
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.87
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.20
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.01
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.94
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.76
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.06
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4750.25
p-value of test                       :    0.9944


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.12
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.81
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:34.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.68
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :   -0.79
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:21.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.76
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -1.37
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:21.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.74e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 6.11e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.72
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.17
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.76
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:04.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:03.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10058.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.50
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:04:11.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.57
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:52.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.62
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:52.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.66
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.01
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11961.23
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.64
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000074446

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.93
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999984656

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:10.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:58.79

 All tests were passed




Server wird beendet - Lösche Semaphor 118784004.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1261
p-value of test                       :    0.9975

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334381
  j =  1                              :        599997478
  j =  2                              :             1261
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:53.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:58.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:05.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:06.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:55.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:00.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    2.44
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     659
p-value of test                       :  9.2e-3

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.34
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:15.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    3.94
p-value of test                       :  9.4e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     116
p-value of test                       :    0.9977

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:46.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.13
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.90
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.69
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.87
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.05
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  375.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.58
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:00.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6995.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:41.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.79
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.05
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:03.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.10
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.94
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4808.34
p-value of test                       :    0.9900


-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:55.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46222
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870222
  j =  1                              :        399907558
  j =  2                              :            46218
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45668
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869668
  j =  1                              :        399908666
  j =  2                              :            45664
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:29.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:17.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:45.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:59.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.39e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.71e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:35.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.010
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.62
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.06
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.78
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.52
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.00
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.48
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   96.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17649.57
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.19
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.09
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.66
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.20
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.85
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.66
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.61
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.19
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.06
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.10
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.48
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.17
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.09
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.49
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.86
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.04
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.44
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.51
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.19
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4836.75
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.70
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.47
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.17
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5297.94
p-value of test                       :  1.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.84
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.40
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.03
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:22.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.73
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:23.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.47e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.91
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.68
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.73
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:05.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:03.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10048.94
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.32
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : 1.07e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:36.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5004.51
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.09
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3983.24
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.25
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12056.39
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11933.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.95
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999775739

Normal statistic for number of bits   :   -1.77
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.18
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999918044

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:38.52

 All tests were passed




Server wird beendet - Lösche Semaphor 119799812.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5560
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:53.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:05.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:06.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7147
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:56.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:00.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.34
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:15.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    2.27
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:45.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.56
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.57
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.24
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.16
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:43.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.09
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:59.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7150.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.15
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.05
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:02.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.40
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.08
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:35.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5087.35
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:00.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46052
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870052
  j =  1                              :        399907899
  j =  2                              :            46046
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45720
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869720
  j =  1                              :        399908562
  j =  2                              :            45716
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:28.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:00.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:55.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:33.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.83e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 8.20e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:33.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.92
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.43
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.80
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.16
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.25
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.78
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.36
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17382.64
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.70
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.02
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.72
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.98
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.86
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.17
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.61
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.81
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.95
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.90
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.10
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.02
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.07
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.17
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.76
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.02
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.90
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.79
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.84
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.35
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.53
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.38
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.69
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.64
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.10
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.32
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.62
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.43
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.18
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.55
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    1.62
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.81
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    1.68
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.66e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 6.91e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.92
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.69
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.50
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:04.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:03.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9974.20
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9757.08
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:39.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.40
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4721.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:50.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.59
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11978.43
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11890.09
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.57
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999962456

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.64
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000081817

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:59.57

 All tests were passed




Server wird beendet - Lösche Semaphor 120815620.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5344
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:53.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:39.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:06.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:57.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:00.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:50.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:14.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:47.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.71
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.67
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.88
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.66
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.68
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.02
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.67
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:43.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.40
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:00.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6836.84
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.09
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:01.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.28
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.69
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5002.94
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:01.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45853
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869853
  j =  1                              :        399908300
  j =  2                              :            45841
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46212
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870212
  j =  1                              :        399907579
  j =  2                              :            46206
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.78e-3
p-value of test                       :    0.9912

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:26.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:17.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:57.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:54.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.49e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 9.85e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.052
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:31.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:32.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.72
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.69
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.17
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.83
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.86
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:50.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.65
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.64
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17425.92
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.26
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.38
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.91
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.77
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.93
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.19
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.00
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.45
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.46
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.80
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.37
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  568.69
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.15
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.14
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.32
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.52
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5174.82
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.76
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.34
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.19
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.21
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.50
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.23
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.90
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:10.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.55
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -1.43
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:09.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.04e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.15e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.73
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.86
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:15.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.42
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:54.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.38
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:53.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10035.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9845.46
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:48.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.47
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:17.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 7.46e-3
p-value of test                       :    0.9920

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4698.09
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.14
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3999.19
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11617.62
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12004.37
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.87
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999928526

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.29
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000053830

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:56:01.69

 All tests were passed




Server wird beendet - Lösche Semaphor 121831428.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5381
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:41.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:36.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:34.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:54.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7117
p-value of test                       :    0.9908


-----------------------------------------------
CPU time used                    :  00:03:01.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:00.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:52.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:59.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.28
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.53
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    2.19
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:10.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:35.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.32
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.11
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.10
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.67
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7059.18
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:45.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   51.08
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.32
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:07.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.37
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.61
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:35.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5130.10
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:17.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46251
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870251
  j =  1                              :        399907501
  j =  2                              :            46245
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45600
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869600
  j =  1                              :        399908805
  j =  2                              :            45590
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:29.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:18.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.28e-3
p-value of test                       :    0.9942

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :  4.2e-3

Anderson-Darling statistic = A2       :    3.77
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:52.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:33.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.95e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 5.54e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:36.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:47.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.20
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.26
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.85
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.80
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.22
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:11.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.69
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.64
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17567.01
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.36
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.32
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   44.62
p-value of test                       :  9.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.04
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.16
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.35
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.10
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.81
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.82
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.80
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.32
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.14
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.13
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.35
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.85
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.47
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.06
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  174.09
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.54
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.31
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.26
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.83
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.95
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.27
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.10
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.89
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.42
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.10
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.94
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.63
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:18.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.13
p-value of test                       :    0.9946


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:15.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.97e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 9.29e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.93
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.80
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.09
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:08.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.90
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:09.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10078.26
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9933.22
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.053
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:48.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4769.30
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.11
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:50.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4245.28
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.42
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11950.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.64
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999949370

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.16
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999992291

Normal statistic for number of bits   :  -0.061
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    2.38
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.15

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:14:24.77

 All tests were passed




Server wird beendet - Lösche Semaphor 101744645.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5477
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:43.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:00.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:01.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7497
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:52.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:57.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.32
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:10.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    2.93
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    2.12
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:39.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.08
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.61
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.86
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.11
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.06
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1550.82
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:02.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6915.00
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.67
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:03.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.82
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:47.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.73
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:34.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4864.57
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:17.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45945
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869945
  j =  1                              :        399908113
  j =  2                              :            45939
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45897
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869897
  j =  1                              :        399908211
  j =  2                              :            45887
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:29.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:45.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:53.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :  4.3e-3

Anderson-Darling statistic = A2       :    3.84
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.73e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.91e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.074
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:35.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.79
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.11
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.62
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.20
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.17
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:43.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.09
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.00
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.5e-3

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17736.88
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.65
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.81
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.96
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.20
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.42
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.67
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.17
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.93
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.30
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.83
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.56
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.52
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.21
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.82
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.01
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.50
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.66
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.79
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.97
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.45
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5113.15
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.73
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.94
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.45
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.30
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.74
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.47
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.05
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.80
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:20.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.52
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:19.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 5.51e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.91
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.88
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.07
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:08.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.64
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.67
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.41
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:53.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.38
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.18
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.98
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11759.10
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11949.72
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.42
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999867152

Normal statistic for number of bits   :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.53
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999992966

Normal statistic for number of bits   :  -0.056
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:56.81

 All tests were passed




Server wird beendet - Lösche Semaphor 102957061.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1466
p-value of test                       :  3.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334586
  j =  1                              :        599997068
  j =  2                              :             1466
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5360
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:46.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:37.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:35.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:54.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:00.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:00.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:52.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:56.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    2.77
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     956
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:45.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:11.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.45
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:10.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:38.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.30
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.99
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.24
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.35
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.70
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.27
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:02.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7014.18
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.74
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.78
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:03.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.45
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:47.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.96
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:33.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5077.29
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:12.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45606
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869606
  j =  1                              :        399908790
  j =  2                              :            45602
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45906
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869906
  j =  1                              :        399908191
  j =  2                              :            45900
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 8.77e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :  3.3e-4    *****

Anderson-Darling statistic = A2       :    6.16
p-value of test                       :  8.5e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  1.0e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:28.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
p-value of test                       :    0.9905

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:01.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-3
p-value of test                       :    0.9985

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:33.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:35.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:34.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.70
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:48.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.80
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.53
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.67
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.64
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:41.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.70
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.79
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17210.84
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.30
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.79
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.65
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.68
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.64
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.61
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.72
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.16
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.16
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  438.55
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  180.63
p-value of test                       :  6.3e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.06
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.68
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.09
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.63
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.90
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.20
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.18
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.82
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.85
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.93
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.82
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.53
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.85
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4919.72
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.91
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.82
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:34.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.75
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    1.98
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:18.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.22
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    1.56
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:20.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.83

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 4.97e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 4.43e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.66
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.04
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.07
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:06.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10035.76
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9819.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.062
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:46.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4799.07
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.99
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.41
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.04
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.04
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000017479

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.03
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000038446

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.72
p-value of test                       :  4.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.99
p-value of test                       :    0.9986

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:39.53

 All tests were passed




Server wird beendet - Lösche Semaphor 103940101.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5500
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:47.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4501
p-value of test                       :  6.7e-3


-----------------------------------------------
CPU time used                    :  00:01:37.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:36.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:54.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4216
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:01.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7157
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:01.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:52.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:57.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    3.40
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    3.21
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    2.54
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:10.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:41.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.97
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.39
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.99
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.44
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.25
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.73
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  473.90
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:45.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1531.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:58.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7071.15
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.48
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:03.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.35
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  156.61
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5247.56
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:57.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45953
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869953
  j =  1                              :        399908098
  j =  2                              :            45945
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45578
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869578
  j =  1                              :        399908845
  j =  2                              :            45576
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:28.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-3
p-value of test                       :    0.9985

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:32.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.26e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:35.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.20
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:47.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.53
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.76
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.17
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:46.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.38
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.84
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.93
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.95
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.078
p-value of test                       :    0.9944

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17437.86
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.14
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.53
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.73
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.28
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.70
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.93
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.35
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.39
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.65
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.70
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.52
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.95
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  175.45
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.64
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.85
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.96
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.35
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.73
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.17
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.24
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.66
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.16
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.58
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.86
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.21
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.44
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.16
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.81
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.53
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.22
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.41
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.63e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 2.30e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.16
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.96
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9909

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.71
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:06.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.87
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9846.67
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:45.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4756.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4774.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.98
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4215.18
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11617.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11680.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:29.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.60
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000060877

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.47
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000129610

Normal statistic for number of bits   :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:07.36

 All tests were passed




Server wird beendet - Lösche Semaphor 104923141.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5416
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:52.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4179
p-value of test                       :    0.9918


-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:37.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:54.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7159
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:01.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:02.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:53.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:57.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:43.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:10.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    2.86
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    3.71
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:38.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.83
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.73
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.37
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.83
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.35
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.71
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.15
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:59.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7176.16
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:41.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.21
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:03.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.44
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.12
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5108.81
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9935


-----------------------------------------------
CPU time used                    :  00:02:55.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45969
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869969
  j =  1                              :        399908067
  j =  2                              :            45959
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45968
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869968
  j =  1                              :        399908066
  j =  2                              :            45964
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:28.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:18.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:44.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:00.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:54.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 4.43e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.64e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.35
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:47.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.80
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.77
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.33
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.01
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.12
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:37.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.08
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.23
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17657.49
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.38
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.50
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.35
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.43
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.08
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.68
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.31
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.70
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.73
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.16
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.51
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.40
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.78
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.12
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.10
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.42
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.01
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.41
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.71
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.42
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.13
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.72
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.83
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.01
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.73
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.25
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.47
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.52
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.89
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.02
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:20.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.89
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.84
p-value of test                       :    0.03

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   0.033
p-value of test                       :    0.49

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.90
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.29
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.12
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:04.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:04.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10126.13
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.94e-3
p-value of test                       :    0.9926

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10326.13
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:46.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.72
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:50.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.65
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11709.25
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12207.62
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.13
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999961025

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.41
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000138031

Normal statistic for number of bits   :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:24.31

 All tests were passed




Server wird beendet - Lösche Semaphor 105807877.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:53.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:37.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:01.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:53.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7470
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:56.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     944
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:43.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    3.31
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     271
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:12.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:39.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.90
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.61
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.55
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.48
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.19
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1361.99
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:00.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6869.78
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.18
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.02
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:04.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.08
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.66
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:32.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5071.01
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:56.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45997
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869997
  j =  1                              :        399908012
  j =  2                              :            45985
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908478
  j =  2                              :            45755
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 9.05e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:28.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:18.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:02.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 8.94e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.20
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:35.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.05
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:47.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.30
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.84
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.23
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.34
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:37.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.15
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.43
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.48
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.94e-3
p-value of test                       :    0.9948

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  167.91
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17533.50
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.25
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.79
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.10
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.69
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.32
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.75
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.91
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.54
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.30
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.05
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  444.66
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.61
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.02
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.18
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.91
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.44
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.48
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.03
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.36
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.84
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.74
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.64
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.92
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:34.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.16
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.61
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.55
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.24
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.27
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:34.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.11
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:19.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.60
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -2.51
p-value of test                       :    0.9940



-----------------------------------------------
CPU time used                    :  00:02:23.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 5.70e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 5.70e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.44
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.58
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.66
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.69e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  154.24
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.01
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9972.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:47.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.29
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:49.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.59
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.29
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11789.41
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.35
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999923624

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.88
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999999428

Normal statistic for number of bits   : -4.52e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:11.75

 All tests were passed




Server wird beendet - Lösche Semaphor 106823685.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5467
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:54.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4439
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:39.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:39.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:54.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:02.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:03.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:53.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:57.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.47
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    4.80
p-value of test                       :  3.6e-3

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.65
p-value of test                       :  4.3e-3

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     335
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    2.46
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:09.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:37.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.31
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.71
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.17
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.11
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.04
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.32
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.80
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.50
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7135.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.65
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.58
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:05.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.67
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.25
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5121.42
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:53.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46087
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870087
  j =  1                              :        399907830
  j =  2                              :            46079
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46035
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870035
  j =  1                              :        399907932
  j =  2                              :            46031
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:27.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :  2.2e-3

Anderson-Darling statistic = A2       :    4.15
p-value of test                       :  7.5e-3


-----------------------------------------------
CPU time used                    :  00:02:17.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:59.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:55.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.19e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.36e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 5.27e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.68
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:34.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.28
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.87
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.98
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:39.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.33
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.51
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.22e-3
p-value of test                       :    0.9945

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16994.47
p-value of test                       :    0.9906



-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.12
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.08
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.71
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.90
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.98
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.36
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.93
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.72
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.99
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.93
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  177.34
p-value of test                       :  9.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.63
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.65
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.08
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.18
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.10
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.24
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.58
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.97
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.45
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.94
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.99
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.37
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.63
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5052.23
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.07
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.78
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.70
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :   -1.10
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:19.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.16
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:19.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    2.46
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.51e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.00
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.34
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.91
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:06.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9827.46
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9903.54
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.85
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.49
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11924.46
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:30.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.19
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000009046

Normal statistic for number of bits   :   0.072
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.38
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000019723

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:52.77

 All tests were passed




Server wird beendet - Lösche Semaphor 107839493.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5494
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:59.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:42.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:04.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:04.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:56.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:59.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.10
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    2.44
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:12.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.04
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    3.46
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     179
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:38.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.49
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.53
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.49
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:11.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.23
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.24
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.73
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  189.91
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  515.07
p-value of test                       :  4.4e-3

-----------------------------------------------
CPU time used                    :  00:01:46.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.46
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:05.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7054.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-3
p-value of test                       :    0.9982

Kolmogorov-Smirnov- statistic = D-    :    0.72
p-value of test                       :  1.9e-3

Anderson-Darling statistic = A2       :    4.13
p-value of test                       :  8.3e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   55.00
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:08.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.78
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.67
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5014.69
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:59.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45916
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869916
  j =  1                              :        399908169
  j =  2                              :            45914
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45797
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869797
  j =  1                              :        399908409
  j =  2                              :            45791
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:29.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:18.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:04.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 8.42e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.23e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 3.34e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.99
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.96
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.23
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.39
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.97
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.88
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:46.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.80
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:39.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17537.22
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.79
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.95
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.53
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.32
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.61
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.23
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.10
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.77
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.09
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.32
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.93
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.80
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.25
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.58
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.32
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.71
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.61
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.80
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.19
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.45
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.30
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.10
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.51
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.47
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.21
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.12
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5136.42
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.79
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.52
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.37
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:21.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.17
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 9.68e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.43e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.66
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.96
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.39
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.31
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:06.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10128.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9739.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:04:22.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:52.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.57
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:53.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3980.19
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.13
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12056.16
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11552.66
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:32.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.73
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999907910

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.02
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000074893

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.20
p-value of test                       :    0.99

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.23
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:13.71

 All tests were passed




Server wird beendet - Lösche Semaphor 108756997.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1222
p-value of test                       : 1 -  4.8e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334342
  j =  1                              :        599997556
  j =  2                              :             1222
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5355
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4483
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:03.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:04.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:55.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:58.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.93
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    3.57
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     269
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:12.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    2.20
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:43.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.01
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.31
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.62
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.26
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.04
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.45
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.55
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.33
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:04.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6993.31
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.05
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:05.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.59
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.66
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:32.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4914.71
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:57.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908163
  j =  2                              :            45917
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45830
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869830
  j =  1                              :        399908342
  j =  2                              :            45826
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:27.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:18.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:45.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:34.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 5.51e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.16e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:32.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.92
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.02
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.03
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.50
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   47.52
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:38.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.37
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.59
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.38
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  167.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.7e-3

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17815.06
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.05
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.84
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.88
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.17
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.98
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.13
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.33
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.88
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.94
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.15
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.90
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.37
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.39
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.75
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.19
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.76
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.47
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.74
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.58
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4896.76
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.53
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.85
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.66
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.75
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5190.41
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.58
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.24
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.34
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -1.41
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:21.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.71
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    1.59
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:22.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.60e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   26.57
p-value of test                       :  8.4e-4    *****

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.03
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:04.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.87
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.76
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10131.97
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:42.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.41e-3
p-value of test                       :    0.9965

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5117.66
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.12
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3998.73
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4198.09
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11915.50
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11695.43
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.53
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000134140

Normal statistic for number of bits   :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.29
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999955925

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.97
p-value of test                       :    0.02

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:17.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14          1 -  4.8e-5
 86  LongestHeadRun, r = 0           8.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 109838341.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:56.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4495
p-value of test                       :  8.6e-3


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:57.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:04.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:04.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:56.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:00.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    3.35
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:12.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:41.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.39
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.62
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.51
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.71
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.47
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.36
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.91
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7092.22
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:43.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.40
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:04.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.36
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.81
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5071.18
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  5.0e-3


-----------------------------------------------
CPU time used                    :  00:02:57.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45842
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869842
  j =  1                              :        399908322
  j =  2                              :            45830
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46039
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870039
  j =  1                              :        399907928
  j =  2                              :            46027
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:27.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:18.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:34.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.78e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.41e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.024
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:33.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:33.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.14
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.69
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.53
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.48
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.77
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
p-value of test                       :    0.9901

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.81
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.09
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17384.96
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.38
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.26
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.27
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.41
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.23
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.45
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.07
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    4.35
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.17
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.07
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.89
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.12
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.01
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.41
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.38
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.15
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.72
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.67
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.23
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.68
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5125.90
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.73
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.76
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.98
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.79
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5109.78
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.48
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.68
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.99
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.09
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.42e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.96e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.64
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.50
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.76
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:06.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.32
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:07.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10021.61
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9984

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:39.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.28
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4702.29
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.74
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.42
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11773.18
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.17
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.69
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000000259

Normal statistic for number of bits   : 2.05e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.25
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999978269

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :  -0.021
p-value of test                       :    0.51

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:07.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 C (L=50, r=25)      0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 110821381.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5552
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:59.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4439
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:45.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:01.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4447
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:01.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:12.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:12.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7511
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:04:09.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:13.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:13.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.20
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.18
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.68
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.37
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.58
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.39
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:57.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:08.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6973.71
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:59.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.88
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:15.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.54
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.14
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4866.38
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:54.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908167
  j =  2                              :            45909
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45853
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869853
  j =  1                              :        399908294
  j =  2                              :            45853
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:29.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:22.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:09.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:57.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:38.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.76e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.63
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:00:25.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:45.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.90
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.57
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:53.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.17
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.63
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17286.65
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.26
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.84
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.98
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.21
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.89
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.60
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.15
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.55
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.17
p-value of test                       :    0.9920


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.38
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.68
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  558.85
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.06
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.31
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.72
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.83
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.79
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.60
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.18
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.27
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.11
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.17
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.16
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.67
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.36
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.27
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.56
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.72
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.66
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.02
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:24.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.36
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:22.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.90e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.16e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 6.23e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.89
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.76
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.19
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.67
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10213.92
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9766.72
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:04:33.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.71
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:51.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4739.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:55.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11941.81
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:33.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.79
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.54
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000036175

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.41
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000021625

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:19.27

 All tests were passed




Server wird beendet - Lösche Semaphor 111837189.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  1.1e-3


-----------------------------------------------
CPU time used                    :  00:00:40.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5500
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:55.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:07.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:01.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:02.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:13.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    2.11
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    2.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:41.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.04
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.87
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.41
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.38
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.56
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.20
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.52
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:49.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:04.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7106.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:54.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   51.45
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.92
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:14.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.22
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.93
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5134.98
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:56.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45762
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869762
  j =  1                              :        399908480
  j =  2                              :            45754
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45565
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869565
  j =  1                              :        399908874
  j =  2                              :            45557
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:30.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:49.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:05.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:57.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.29e-3
p-value of test                       :    0.9916

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:39.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.94e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:40.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:41.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.07
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.34
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.71
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.54
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.81
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.00
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.19
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17558.83
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.54
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.93
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.15
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.60
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.57
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.59
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.50
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.98
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.63
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.18
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.63
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.50
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.97
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.47
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.30
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.19
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.74
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.27
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.29
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.45
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.40
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.64
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.66
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.84
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  464.46
p-value of test                       :  3.0e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.14
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.70
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  155.39
p-value of test                       :    0.9915


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.28
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:21.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.48
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :  -0.064
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:23.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 2.35e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.55e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 9.36e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.15
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.80
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:05.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.49
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:06.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9904.93
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10114.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:04:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.28
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.55
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.45
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.94
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11801.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:33.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11590.90
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:34.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.09
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999879431

Normal statistic for number of bits   :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.69
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999927053

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.23
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:22.35

 All tests were passed




Server wird beendet - Lösche Semaphor 113147909.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:53.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7490
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4487
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:04.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:03.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:53.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:59.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     828
p-value of test                       :    0.9920

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:45.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    2.15
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:13.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    2.42
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:42.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.16
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.39
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.54
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.27
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.66
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.89
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:02.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7290.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.70
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:04.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5134.72
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:55.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45913
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869913
  j =  1                              :        399908179
  j =  2                              :            45903
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45974
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869974
  j =  1                              :        399908055
  j =  2                              :            45968
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:28.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  9.1e-3

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:59.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:34.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 5.26e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.58
p-value of test                       :  4.9e-3

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.084
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.81
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.70
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.23
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.58
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.06
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.49
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.04
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.11
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17512.75
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.38
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.01
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.77
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.57
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.59
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.89
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.84
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.45
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.79
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.39
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.57
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.22
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.07
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.97
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.16
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.85
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.52
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.59
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.54
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.50
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.46
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.03
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.25
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.97
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.29
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.40
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.66
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.16
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.98
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.28
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    1.34
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.69
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:22.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.70e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 5.52e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   22.63
p-value of test                       :  3.9e-3

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.05
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.48
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.75
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.73
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:41.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4719.83
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:50.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.06
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4028.21
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11667.95
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11668.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.63
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000158296

Normal statistic for number of bits   :    1.25
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.18
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000085042

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    2.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :  -0.055
p-value of test                       :    0.52

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:45.44

 All tests were passed




Server wird beendet - Lösche Semaphor 114229253.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5447
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:56.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4459
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7509
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:39.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:57.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:05.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:04.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:53.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:58.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.93
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:45.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    2.24
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:12.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.69
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.16
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.38
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.34
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.71
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.59
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.22
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.85
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:02.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7012.87
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:41.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.50
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.08
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:03.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.58
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.04
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:33.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4999.77
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:55.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46072
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870072
  j =  1                              :        399907862
  j =  2                              :            46060
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45955
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869955
  j =  1                              :        399908092
  j =  2                              :            45951
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:26.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.93e-3
p-value of test                       :    0.9900

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:17.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:34.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.49e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.045
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.06
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.59
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.86
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.01
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.04
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.02
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.74
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.86
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.69
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17458.94
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:52.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.87
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.63
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.86
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.64
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.35
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.05
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.43
p-value of test                       :    0.9904


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.76
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.30
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.05
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.49
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.80
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.35
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.29
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.90
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.18
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.05
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.08
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.09
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.72
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.52
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.00
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5179.15
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.87
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.12
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.79
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.81
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.08
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.90
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.34
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.84
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    0.66
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:23.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.86
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:22.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.11
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.53
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:05.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.92
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10119.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.60
p-value of test                       :  3.0e-4    *****

Anderson-Darling statistic = A2       :    4.20
p-value of test                       :  7.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10361.71
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.089
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:40.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:48.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:50.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4347.05
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.86
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11580.72
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11797.64
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:29.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.68
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000040048

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.50
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999862751

Normal statistic for number of bits   :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 4.84e-3
p-value of test                       :    0.9949

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:43.54

 All tests were passed




Server wird beendet - Lösche Semaphor 115179525.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1498
p-value of test                       :  1.9e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334618
  j =  1                              :        599997004
  j =  2                              :             1498
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5333
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:06.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:05.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:55.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:00.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     943
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:16.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:46.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.64
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.23
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.62
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.13
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.03
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.47
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.79
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1503.30
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:01.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7018.59
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:03.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.12
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.15
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:32.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4953.11
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:58.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46050
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870050
  j =  1                              :        399907903
  j =  2                              :            46044
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46054
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870054
  j =  1                              :        399907893
  j =  2                              :            46052
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:27.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9912


-----------------------------------------------
CPU time used                    :  00:02:18.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:36.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:35.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.20
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.96
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.78
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.33
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.87
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.21
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.41
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.62
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17497.20
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.17
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.17
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.44
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.46
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.36
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.18
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.63
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.53
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.05
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.85
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.39
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.17
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.93
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.10
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.71
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.97
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.19
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.42
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.74
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.96
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.03
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.28
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.05
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.31
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.06
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.11
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.50
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.74
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.68
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:21.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.84
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:22.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    2.36
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.71e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 9.05e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.12
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.47
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.75
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:06.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9670.93
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10110.03
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:37.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9907

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.70
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.49
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:50.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4024.01
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11712.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11773.81
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.95
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999955718

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.52
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999860732

Normal statistic for number of bits   :   -1.10
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:35.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           1.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 116162565.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9913


-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5406
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:57.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:43.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:11.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:08.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:02.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:03.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.15
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     849
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:54.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:18.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.89
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.91
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:47.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.28
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.35
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.54
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.02
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.07
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.02
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  289.81
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.60
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.58
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:04.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7110.41
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:52.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.42
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.59
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:14.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.26
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.38
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:38.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4920.01
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45773
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869773
  j =  1                              :        399908458
  j =  2                              :            45765
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45738
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869738
  j =  1                              :        399908531
  j =  2                              :            45724
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:30.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  6.1e-3

Anderson-Darling statistic = A2       :    3.60
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:19.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:06.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.81e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.61e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.41
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.06
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.78
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.36
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.07
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.50
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.01
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17438.34
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.21
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.88
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.91
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.13
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.04
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.59
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.61
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.11
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.98
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.86
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.71
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.61
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.77
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.97
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.63
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.15
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.32
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.60
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.12
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4913.53
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.94
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.39
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.08
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.96
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.82
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.46
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.66
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.55
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -1.44
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:25.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.92
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :    2.09
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:24.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.24e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.95e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 7.32e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.37
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.15
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.32
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:05.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9840.03
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10130.76
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.086
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:04:28.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5044.09
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:53.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.11
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.00
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11887.51
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11804.56
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.02
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999850244

Normal statistic for number of bits   :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.00
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000012010

Normal statistic for number of bits   :   0.095
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.18
p-value of test                       :    0.99

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:14.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:12.51

 All tests were passed




Server wird beendet - Lösche Semaphor 117178373.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5399
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:56.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:41.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:57.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:05.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:05.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:55.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7188
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:00.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:50.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.15
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.96
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9968

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:17.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:48.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.47
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.57
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   88.79
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.72
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.58
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.55
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7042.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.24
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.03
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:03.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.17
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.03
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:33.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5081.91
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:16.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45702
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869702
  j =  1                              :        399908602
  j =  2                              :            45690
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46153
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870153
  j =  1                              :        399907698
  j =  2                              :            46145
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:28.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:18.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 5.77e-3
p-value of test                       :    0.9936

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:54.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.71e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.78e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.62
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.36
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.76
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.14
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.60
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.38
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.55
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.57
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17604.72
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.56
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.14
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.46
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.80
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.16
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.68
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.52
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.86
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.78
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.88
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.15
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.98
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.65
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.58
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.58
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.91
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.60
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.42
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  310.84
p-value of test                       :    0.9975


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.88
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5082.11
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.97
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.79
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.74
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.43
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.62
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.97
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.29
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.76
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.51
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -1.10
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.04e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 5.22e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.20e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.80
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.32
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:06.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9671.88
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9878.46
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:37.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4743.01
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:50.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.03
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:50.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.71
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.56
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.09
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11818.10
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.49
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999883763

Normal statistic for number of bits   :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.47
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000032185

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :  -0.095
p-value of test                       :    0.54

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:51.89

 All tests were passed




Server wird beendet - Lösche Semaphor 118292485.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5570
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:55.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:05.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:05.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:55.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:04:01.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:15.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.91
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.83
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.20
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7069.86
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   50.94
p-value of test                       :  9.9e-3

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.57
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:04.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.93
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.56
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5058.37
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:01.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45716
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869716
  j =  1                              :        399908572
  j =  2                              :            45708
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45904
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869904
  j =  1                              :        399908194
  j =  2                              :            45900
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.38e-3
p-value of test                       :    0.9902

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:28.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:01.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:55.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:35.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 9.20e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.17
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.69
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:47.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.75
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.58
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.84
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.46
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17310.23
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.54
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.18
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.01
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.33
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.61
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.93
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.76
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.21
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.97
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.86
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  192.60
p-value of test                       :  5.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.42
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.39
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.98
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.01
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.10
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.54
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.82
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.73
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.22
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.34
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.65
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.55
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.33
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.95
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4922.77
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.53
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  249.96
p-value of test                       :  9.4e-3


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.43
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:23.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.07
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:22.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.64e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.98e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 8.39e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.62
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.49
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.29
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:04.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:07.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10228.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.60
p-value of test                       :  3.0e-4    *****

Anderson-Darling statistic = A2       :    6.26
p-value of test                       :  8.0e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10444.71
p-value of test                       :  9.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:35.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.62
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.12
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:50.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.42
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.62
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11716.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.80
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000012022

Normal statistic for number of bits   :   0.095
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.60
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999925016

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.73
p-value of test                       :    0.04

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:13.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 91  HammingWeight2, r = 27          9.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 119308293.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:10.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5433
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:41.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:58.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:05.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7512
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:04.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:55.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:59.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.81
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     857
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:14.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.87
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:46.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.12
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.07
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.59
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.88
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1406.34
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:02.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6951.78
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.02
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:05.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.89
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.49
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:33.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4983.38
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:00.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45595
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869595
  j =  1                              :        399908811
  j =  2                              :            45593
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45964
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869964
  j =  1                              :        399908075
  j =  2                              :            45958
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:28.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:19.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:01.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:54.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:34.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:35.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.18
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.37
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.87
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.21
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.96
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:42.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.96
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.80
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17518.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.92
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.16
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.02
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.91
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.75
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.78
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.04
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.17
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.44
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.85
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.89
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.51
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.36
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.56
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.05
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.24
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.73
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.00
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.78
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.47
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.33
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.76
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.52
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.93
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.18
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.21
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5196.14
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.39
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.79
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.27
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    1.72
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.35
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    2.08
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:24.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    2.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.75e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.67e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.59
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.17
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.21
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:04.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.16
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:06.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9833.39
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10110.00
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:36.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.19
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5015.38
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:51.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4013.23
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11666.76
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11766.74
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.19
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999848087

Normal statistic for number of bits   :   -1.20
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.27
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000013564

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.060
p-value of test                       :    0.48

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.084
p-value of test                       :    0.53

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:00.72

 All tests were passed




Server wird beendet - Lösche Semaphor 120291333.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9963


-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5364
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:57.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4465
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:05.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:55.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:00.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    2.03
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    4.10
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:11.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.87
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:42.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.84
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.08
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.35
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.99
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.58
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.60
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  476.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:44.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1508.50
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:03.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7269.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   48.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.56
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:05.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.40
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.63
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:32.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4991.64
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:58.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45801
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869801
  j =  1                              :        399908404
  j =  2                              :            45789
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45810
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869810
  j =  1                              :        399908386
  j =  2                              :            45798
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:27.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:33.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.56e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.82e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.98
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.73
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.62
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:38.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.29
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17137.72
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.56
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.40
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.81
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.45
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.11
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.54
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.10
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.54
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.98
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.57
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.83
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.36
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.88
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.85
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.66
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.28
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.83
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.51
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.40
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.35
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.27
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.57
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  152.96
p-value of test                       :    0.9943


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.87
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.64
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.57
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.35
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.22
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.61
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:20.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.78
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :   -0.82
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:20.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 5.56e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.69e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 9.60e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.11
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.93
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9964.40
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10084.04
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:31.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.66
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:38.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:38.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.54
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3980.07
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11618.04
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11983.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.69
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000090022

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.82
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999979163

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 9.26e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.15
p-value of test                       :    0.98

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:00:10.40

 All tests were passed




Server wird beendet - Lösche Semaphor 121307141.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5451
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:42.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:35.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:33.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:54.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:54.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:01.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:00.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:52.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:58.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    2.46
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:12.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:35.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.14
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.54
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.10
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.88
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.99
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.85
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  392.76
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.39
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:00.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7099.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.13
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.98
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:03.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.55
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.40
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:34.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4954.04
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:03.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45835
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869835
  j =  1                              :        399908334
  j =  2                              :            45827
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46242
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870242
  j =  1                              :        399907518
  j =  2                              :            46238
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:31.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:19.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:59.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.35e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.39e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:48.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.67
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   98.42
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.30
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.27
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.47
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:41.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.94
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.08
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17619.90
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.27
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.04
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.07
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.94
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.48
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.04
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.94
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.78
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.16
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.79
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.35
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.34
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.23
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.75
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.26
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.33
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.55
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.67
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.17
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.78
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.33
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.05
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.58
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.95
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.80
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5197.23
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.79
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.98
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :    1.46
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:28.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.00
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:20.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.69e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.39
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.73
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.08
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:08.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9679.47
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9801.71
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:44.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.00
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.05
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4239.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4283.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11814.11
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12103.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.76
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999999782

Normal statistic for number of bits   : -1.72e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.85
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000154807

Normal statistic for number of bits   :    1.22
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.68

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:47.57

 All tests were passed




Server wird beendet - Lösche Semaphor 101777414.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:10.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1476
p-value of test                       :  1.5e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334596
  j =  1                              :        599997048
  j =  2                              :             1476
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:44.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4459
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:36.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:35.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:54.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:03.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:03.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:58.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:01.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    2.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:10.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.43
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:39.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.36
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.94
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.04
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.02
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:29.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  470.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.22
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:07.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7011.21
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.43
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    3.67
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.37
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.95
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.58
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:41.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5072.72
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:07.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45423
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869423
  j =  1                              :        399909157
  j =  2                              :            45417
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45853
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869853
  j =  1                              :        399908303
  j =  2                              :            45835
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:32.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:20.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 5.42e-3
p-value of test                       :    0.9940

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.46
p-value of test                       :  5.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  1.5e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:02.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:55.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:38.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.28e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.83
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.96
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.81
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.58
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.89
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.17
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:50.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.0e-3

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.71
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.52e-3
p-value of test                       :    0.9920

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17479.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.14
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.63
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.15
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.08
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.00
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.93
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.29
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.30
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.84
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.10
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.04
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.79
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.16
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.00
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.65
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.50
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.64
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.99
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.80
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.50
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.52
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.29
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.70
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.30
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.40
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.31
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4870.05
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.20
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.74
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.79
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:26.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.59
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:27.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.46e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.32
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.48
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.08
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.29
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:08.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9651.81
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9908.46
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:04:28.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4706.15
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5031.58
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:59.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3973.91
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.89
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11851.64
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:34.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11738.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:35.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.05
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000036649

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.94
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000086989

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    2.54
p-value of test                       :  6.6e-3

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:54.31

 All tests were passed




Server wird beendet - Lösche Semaphor 102629398.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5363
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:48.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:38.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:37.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:02.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:02.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:54.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:01.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    2.23
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    5.09
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:01:48.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.55
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:08.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:35.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.49
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.30
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.61
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.69
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  364.63
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.44
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:00.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7137.96
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.91
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:03.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.84
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  148.07
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:34.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4977.62
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:56.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908146
  j =  2                              :            45921
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45778
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869778
  j =  1                              :        399908446
  j =  2                              :            45774
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 7.20e-4
p-value of test                       :    0.9993    *****

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:26.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:18.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:02.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.66
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.08
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.71
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.29
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.83
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.86
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17392.43
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.25
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.31
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.97
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.15
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.16
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.37
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.87
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.48
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.43
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  441.62
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.77
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.10
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.43
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.30
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.32
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.01
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.06
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.78
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.69
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5130.57
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.95
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.57
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.88
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.09
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.93
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.05
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.09
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.40
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.85
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:24.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    2.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.03e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.49e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.93
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.54
p-value of test                       :    0.9920

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.77
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:07.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.93e-3
p-value of test                       :    0.9980

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.71
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9913.05
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9900.78
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:43.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.32
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.0e-3

Kolmogorov-Smirnov- statistic = D-    : 4.60e-3
p-value of test                       :    0.9952

Anderson-Darling statistic = A2       :    4.56
p-value of test                       :  4.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4593.87
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.51
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11752.64
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.44
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.30
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999981452

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.92
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000009631

Normal statistic for number of bits   :   0.076
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
p-value of test                       :    0.9901

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:13.42

 All tests were passed




Server wird beendet - Lösche Semaphor 104366102.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  2.1e-3


-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1270
p-value of test                       :    0.9948

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334390
  j =  1                              :        599997460
  j =  2                              :             1270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5308
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:48.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:38.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4477
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:02.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:02.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:52.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:00.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     953
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.96
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:14.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.86
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:43.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.81
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.46
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.59
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.51
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.15
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1514.66
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6965.90
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:41.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.74
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:03.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.59
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.49
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:33.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5166.76
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:55.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45509
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869509
  j =  1                              :        399908988
  j =  2                              :            45497
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46010
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870010
  j =  1                              :        399907983
  j =  2                              :            46004
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:26.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :  4.1e-3

Anderson-Darling statistic = A2       :    3.91
p-value of test                       :  9.7e-3


-----------------------------------------------
CPU time used                    :  00:02:18.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:33.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.49e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.90e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.069
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:32.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.85
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.27
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.81
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.58
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.80
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.91
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.72
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    4.53
p-value of test                       :  5.1e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   18.93
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.30
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17483.21
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.83
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.69
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.55
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.51
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.44
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.37
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.03
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.47
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.14
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.90
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.31
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  572.90
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.76
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.54
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.59
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.27
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.26
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.56
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.51
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.47
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.64
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.06
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.12
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.88
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.79
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.79
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.66
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.64
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :  -0.086
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:21.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.13
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
p-value of test                       :    0.9901

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.35e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.04e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.60
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.38
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.92
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:08.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.24
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:09.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.12e-3
p-value of test                       :    0.9968

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9659.58
p-value of test                       :    0.9925

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.14
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.063
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:41.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.90
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.07
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4220.92
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.91
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11622.17
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.60
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.03
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999956759

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.50
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000036136

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    2.55
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    2.45
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:12.54

 All tests were passed




Server wird beendet - Lösche Semaphor 105283606.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5360
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:50.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4230
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:59.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:07.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:06.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:53.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:00.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.89
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    2.12
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:13.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.42
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:43.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.54
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.47
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.62
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.26
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.89
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.98
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:58.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.72
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:59.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7070.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:05.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.97
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.82
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:02.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.67
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:00.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45747
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869747
  j =  1                              :        399908509
  j =  2                              :            45741
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45613
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869613
  j =  1                              :        399908777
  j =  2                              :            45607
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:27.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:55.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 8.98e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:32.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.86
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.55
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.70
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.35
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:37.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.18
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.11
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9994    *****

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17451.30
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.38
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.95
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.03
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.47
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.09
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.67
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.07
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.62
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.71
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.82
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.29
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.39
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.25
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  105.14
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.67
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.26
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.09
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.17
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.06
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.20
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  319.59
p-value of test                       :    0.9927


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.86
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.61
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.43
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  461.96
p-value of test                       :  3.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.37
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4886.18
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.87
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.39
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.75
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -1.90
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:22.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.16
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :    1.73
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.82e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.56
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.42
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.06
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:14.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:14.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10136.70
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10133.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:43.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4789.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :  6.1e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    6.25
p-value of test                       :  8.0e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4565.71
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4223.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.23
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11889.15
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.51
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.47
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999987023

Normal statistic for number of bits   :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.98
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000211030

Normal statistic for number of bits   :    1.67
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:35.13
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 96  HammingIndep, L=30, r=27        0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 106201110.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:49.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:39.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:03.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:02.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:54.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:01.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.14
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    2.15
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     650
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.04
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:13.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:37.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.67
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.03
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.43
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.97
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.68
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.35
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.03
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1514.28
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:06.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7141.55
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.83
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:09.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.84
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  159.24
p-value of test                       :  8.1e-3


-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4945.51
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:56.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45976
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869976
  j =  1                              :        399908059
  j =  2                              :            45954
  j =  3                              :               11
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45630
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869630
  j =  1                              :        399908743
  j =  2                              :            45624
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 9.14e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:29.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:18.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:03.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:35.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.38e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 7.32e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.056
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.072
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:42.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.31
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.45
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.15
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.97
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.25
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.01
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.98
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.91
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17537.87
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.58
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.68
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.93
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.14
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.13
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.39
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.18
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.00
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.02
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.01
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.18
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.31
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.25
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.46
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.83
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.55
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.85
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.27
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.15
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.79
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.15
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.28
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.00
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.97
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.55
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.63
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.58
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.84
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.14
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.23
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:25.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.07
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:24.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    2.37
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.12e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.45e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.54
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.10
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:07.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.16
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:07.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.40
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10274.43
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:04:25.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4761.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:52.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.24
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:54.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3843.79
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11402.67
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:01:32.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.86
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999981674

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.76
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000112159

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.012
p-value of test                       :    0.50

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:36.03

 All tests were passed




Server wird beendet - Lösche Semaphor 107118614.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5484
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:51.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:38.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:01.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:54.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:59.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:04.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    4.61
p-value of test                       :  4.4e-3

Stat. AD after spacings (mNP2-S)      :    2.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:14.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:43.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.51
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.13
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.94
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.47
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.59
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:02.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7192.93
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.70
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:03.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.62
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.25
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:36.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4941.77
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:58.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45982
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869982
  j =  1                              :        399908040
  j =  2                              :            45974
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46127
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870127
  j =  1                              :        399907752
  j =  2                              :            46115
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:33.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:26.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:08.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:55.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:32.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:35.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.28
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.60
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.62
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.95
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.43
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.32
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.17
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.02
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.65
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17311.49
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.68
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.26
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.13
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.73
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.52
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.84
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.08
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.56
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.36
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.59
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.09
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.19
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.61
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.59
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.13
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.71
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.34
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.33
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.88
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.73
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.09
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.28
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.99
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.87
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.03
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.98
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.59
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.51
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.33
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.20
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.00
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:25.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.55
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:25.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.53e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.01e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 9.13e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.19
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.07
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:04.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.82
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:06.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10147.97
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.4e-3

Anderson-Darling statistic = A2       :    5.21
p-value of test                       :  2.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10383.59
p-value of test                       :  3.6e-3

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:04:27.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.89
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.02
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11969.81
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12010.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.52
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000008926

Normal statistic for number of bits   :   0.071
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.82
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000021889

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:44.81

 All tests were passed




Server wird beendet - Lösche Semaphor 108199958.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5416
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:52.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:41.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4156
p-value of test                       :    0.9971


-----------------------------------------------
CPU time used                    :  00:01:57.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4471
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7484
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:07.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:08.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:02.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7102
p-value of test                       :    0.9944


-----------------------------------------------
CPU time used                    :  00:04:05.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.06
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    2.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    3.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:13.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.43
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.16
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.59
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.08
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.12
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:29.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.24
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:56.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1520.51
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:07.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7011.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.24
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:18.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.62
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.39
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:39.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5085.37
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:00.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46177
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870177
  j =  1                              :        399907647
  j =  2                              :            46175
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45956
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869956
  j =  1                              :        399908092
  j =  2                              :            45948
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.80e-3
p-value of test                       :    0.9927

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:31.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:17.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:02.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.95e-3
p-value of test                       :    0.9909

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:38.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.67e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.55
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.36
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.05
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.30
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.98
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17482.80
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.33
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.31
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.96
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.33
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.57
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.74
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.12
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.85
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.56
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.17
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.42
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.93
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.79
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.48
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.54
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.74
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.41
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.50
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.89
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.09
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.87
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.11
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.21
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.65
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.02
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.76
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.89
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.21
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.13
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.26
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.26
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:24.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.06e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.93e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.34
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.47
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.3e-3

Anderson-Darling statistic = A2       :    3.91
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  247.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:07.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.20
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:08.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.17
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.15
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:04:25.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.96
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:56.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.13
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11714.76
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:36.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11544.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:36.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.14
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000072526

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.98
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000109489

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:50.63

 All tests were passed




Server wird beendet - Lösche Semaphor 109150230.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5525
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:52.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:55.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:57.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:03.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:03.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:56.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:01.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.14
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:13.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.99
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:41.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.61
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.34
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.02
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.00
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.81
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:43.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.90
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:02.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6995.64
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:44.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.07
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.24
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:04.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.42
p-value of test                       :    0.9948


-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.03
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5134.99
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:08.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45953
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869953
  j =  1                              :        399908101
  j =  2                              :            45939
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46300
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870300
  j =  1                              :        399907401
  j =  2                              :            46298
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:26.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:18.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:01.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:33.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.71e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.05e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:36.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:35.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  106.15
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.34
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.47
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.21
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.63
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.09
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.41
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.05
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.93
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17342.92
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.73
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.51
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.18
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.10
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.99
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.26
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.14
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.47
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.38
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.35
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.69
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.98
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.75
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.08
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.14
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.08
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.76
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.70
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.73
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.59
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.39
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.16
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.31
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.89
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.91
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4922.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.01
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.53
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.52
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.89
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:24.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.17
p-value of test                       :    0.02

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.32e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.41e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.42
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.75
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.75
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.83
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:06.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9879.19
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10148.75
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:41.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.73
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.12
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:50.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.11
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4324.77
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11987.53
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11735.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.21
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999932009

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.45
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999999695

Normal statistic for number of bits   : -2.41e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.81
p-value of test                       :    0.04

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.87e-3
p-value of test                       :    0.9971

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.52
p-value of test                       :  5.9e-3

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:02.75

 All tests were passed




Server wird beendet - Lösche Semaphor 110460950.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1462
p-value of test                       :  4.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334582
  j =  1                              :        599997076
  j =  2                              :             1462
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5362
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:52.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:04.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:04.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:55.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:00.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     853
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9928

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:12.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:42.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.55
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.25
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.63
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.47
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.03
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:44.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1496.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:00.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7092.17
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:40.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.46
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.69
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:05.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.96
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.86
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5029.39
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:03.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46062
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870062
  j =  1                              :        399907880
  j =  2                              :            46054
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46149
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870149
  j =  1                              :        399907706
  j =  2                              :            46141
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  2.0e-3

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:27.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:17.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:44.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.64
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.42
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:01:34.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:33.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.80
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.71
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.58
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.91
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:39.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.41
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.51
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.02
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.46
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17502.78
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.65
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.48
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.36
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.16
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.02
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.20
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.68
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.17
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.84
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.73
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.79
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.44
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.82
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.25
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.13
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.78
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.54
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.78
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.76
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.93
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.43
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.26
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.02
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.80
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.49
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4853.74
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.65
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.93
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.07
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:22.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.75
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:23.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.37e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 8.42e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.85e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.27
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.98
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:06.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  246.07
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:06.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10179.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.79
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.019
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:41.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.65
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4990.27
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4208.52
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11765.17
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11602.38
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.76
p-value of test                       :    0.9901


-----------------------------------------------
Total number of bits:  8000001936

Normal statistic for number of bits   :   0.015
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.60
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999912263

Normal statistic for number of bits   :   -0.69
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         : 5.22e-3
p-value of test                       :    0.50

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:16.69

 All tests were passed




Server wird beendet - Lösche Semaphor 111411222.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5530
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:52.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4489
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:38.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:04.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:54.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:59.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9970


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:13.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:41.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.58
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.65
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.42
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.63
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.08
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.22
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.05
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.92
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7026.43
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:41.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:02.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.56
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.89
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4977.04
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:05.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45506
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869506
  j =  1                              :        399908991
  j =  2                              :            45500
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45963
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869963
  j =  1                              :        399908075
  j =  2                              :            45961
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:27.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:55.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:32.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:35.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.35
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.58
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.37
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.22
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.88
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.39
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:38.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.26
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.33
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.75
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17577.53
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.65
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.75
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.65
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.37
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.41
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.15
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.49
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.10
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.20
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.64
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.80
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.34
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.98
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.64
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.54
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.06
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.08
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.47
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.11
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.15
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.76
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5158.12
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.12
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.54
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.75
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.90
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.18
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.19
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.63
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.33
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:23.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.73e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 9.02e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.85
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.55
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:05.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10157.33
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:39.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:48.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.91
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.83
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12110.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11584.49
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:29.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.68
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000065578

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.26
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999917918

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.07
p-value of test                       :    0.02

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:18.45

 All tests were passed




Server wird beendet - Lösche Semaphor 112361494.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:52.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:39.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:07.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:08.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:01.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:02.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.70
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:15.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:43.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.69
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.83
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.56
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.10
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.56
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.28
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1543.30
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:06.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7093.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.11
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.68
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:15.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   18.80
p-value of test                       :  2.1e-3


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.50
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:37.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.15
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:00.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46283
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870283
  j =  1                              :        399907439
  j =  2                              :            46273
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45902
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869902
  j =  1                              :        399908199
  j =  2                              :            45896
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:29.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:19.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:50.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:07.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:37.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.22e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 4.86e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.06e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.90
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.27
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.07
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.69
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.70
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.51
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.79
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17364.95
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.39
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.06
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.03
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.17
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.06
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.56
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.20
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.25
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.01
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.65
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.16
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.21
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.00
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.56
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.75
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.33
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.42
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.77
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.06
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.15
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.24
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.74
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.70
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.13
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.28
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5166.86
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.47
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.10
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.48
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:24.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.01
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -1.71
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:23.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.61
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.19
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.91
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:06.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:10.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10025.30
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9784.25
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:04:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.88
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5071.45
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.87
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.90
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11643.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:32.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11946.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.81
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999939731

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.39
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000013063

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :  -0.080
p-value of test                       :    0.53

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:49.00

 All tests were passed




Server wird beendet - Lösche Semaphor 113311766.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:53.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:06.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:06.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:01.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:05.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:14.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:42.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.68
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   19.96
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.81
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.93
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.71
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.26
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.51
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1370.37
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:05.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7071.82
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.30
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:15.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.65
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.80
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:38.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5130.20
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:03.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45977
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869977
  j =  1                              :        399908049
  j =  2                              :            45971
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45690
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869690
  j =  1                              :        399908624
  j =  2                              :            45682
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.97e-3
p-value of test                       :    0.9909

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:32.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:20.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9925

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:37.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.090
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.83
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.09
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.98
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.47
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.73
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.61
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.28
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.65
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.64
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17424.75
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.89
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.73
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.69
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.67
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.64
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.97
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.91
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.98
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.85
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.77
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.53
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.33
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.53
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.69
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.30
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.22
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.16
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.36
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.19
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.41
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.16
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.49
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5146.16
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.85
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.62
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.71
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4844.79
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.69
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.04
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.45
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:22.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.93
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :  -0.049
p-value of test                       :    0.52

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.55e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 9.84e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.41e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.63
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.26
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.91
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:04.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.38
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10127.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.080
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:04:17.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4812.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:54.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.1e-3

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5055.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.14
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:33.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11682.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.25
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999965297

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.88
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000102610

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:10.85

 All tests were passed




Server wird beendet - Lösche Semaphor 114393110.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1250
p-value of test                       :    0.9991    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334370
  j =  1                              :        599997500
  j =  2                              :             1250
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5354
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:51.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:39.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:07.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:07.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:06.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:07.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:46.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    2.13
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:12.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:41.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.87
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.21
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.92
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.93
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.27
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.15
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.34
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:06.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6955.17
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:57.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.15
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.56
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.56
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:37.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5035.10
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:01.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45672
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869672
  j =  1                              :        399908657
  j =  2                              :            45670
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908165
  j =  2                              :            45913
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:32.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
p-value of test                       :    0.9902

Anderson-Darling statistic = A2       :    4.12
p-value of test                       :  7.7e-3


-----------------------------------------------
CPU time used                    :  00:02:20.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 2.20e-3
p-value of test                       :    0.9977

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:05.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:37.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.88e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    4.05
p-value of test                       :  2.6e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.08
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.29
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.69
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.16
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.08
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.63
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17562.50
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.04
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.91
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.34
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.79
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.75
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.37
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.60
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.88
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.83
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.30
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.97
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.90
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.54
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.64
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.66
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.45
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.45
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.82
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.83
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5163.55
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.65
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.66
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.62
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.25
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.38
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.90
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.98
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :  -0.010
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.77
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    2.26
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:02:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.29e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.60
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   22.42
p-value of test                       :  4.2e-3

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.93
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.81
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:04.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.69
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10122.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:04:18.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.59
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
p-value of test                       :    0.9926

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4705.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4252.63
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.18
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11700.94
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:33.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.42
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000076528

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.59
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000008644

Normal statistic for number of bits   :   0.068
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:45.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9991 
 57  AppearanceSpacings, r = 0       2.6e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 115507222.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5499
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:55.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:43.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4519
p-value of test                       :  3.0e-3


-----------------------------------------------
CPU time used                    :  00:02:02.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:12.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7522
p-value of test                       :  9.0e-3


-----------------------------------------------
CPU time used                    :  00:04:10.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:14.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    3.76
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:14.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:43.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.77
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.23
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.83
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.46
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.16
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:59.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:07.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7052.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.01
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.18
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  165.73
p-value of test                       :  3.0e-3


-----------------------------------------------
CPU time used                    :  00:01:41.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5037.94
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:55.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46019
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870019
  j =  1                              :        399907962
  j =  2                              :            46019
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46125
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870125
  j =  1                              :        399907752
  j =  2                              :            46121
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:30.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:24.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:52.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:09.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:56.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:38.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 7.22e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.54e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 9.97e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:51.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:53.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.29
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.38
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.80
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.02
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:53.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.08
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.78
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.36
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17400.27
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.71
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.14
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.86
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.12
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.42
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.75
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.42
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.58
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.59
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.66
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.33
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.88
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.21
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.59
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.49
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.01
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.06
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.71
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.61
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.60
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.13
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.03
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.48
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.58
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.55
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.38
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.17
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.03
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.30
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.05
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.39
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -1.40
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:20.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.24
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:21.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         : 5.43e-3
p-value of test                       :    0.50

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 3.74e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.83e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.54
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.08
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.30
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:10.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  243.80
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:12.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.62
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10156.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:11.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:04:31.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4769.46
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:52.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.74
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11930.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:34.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.14
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.62
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000044407

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.91
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000060166

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.11
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:48.45

 All tests were passed




Server wird beendet - Lösche Semaphor 116555798.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5486
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:55.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4239
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7481
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:04.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:54.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:00.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:16.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:45.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.99
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.30
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.43
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.60
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:43.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.42
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6880.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:43.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.39
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.91
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:02.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.82
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.24
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:35.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4979.97
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:59.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45883
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869883
  j =  1                              :        399908238
  j =  2                              :            45875
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45809
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869809
  j =  1                              :        399908384
  j =  2                              :            45805
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.00e-3
p-value of test                       :    0.9966

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  8.0e-3

Anderson-Darling statistic = A2       :    4.21
p-value of test                       :  6.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  1.7e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:28.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:20.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:34.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.59e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:37.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.73
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:48.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.38
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.59
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.98
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.94
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:38.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.75
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.93
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.28
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17563.48
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.41
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.34
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.15
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.47
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.21
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.74
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.76
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.26
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.47
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.11
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.24
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.60
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.17
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:42.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.33
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.79
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.24
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.55
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.66
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.60
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.42
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.03
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.86
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.59
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5160.08
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.39
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.21
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.67
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -1.00
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:22.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.15
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:21.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.90
p-value of test                       :    0.97

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.35e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.32
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.72
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.45
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:03.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:04.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9916.44
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9922.63
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:40.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4994.14
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.27
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.56
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11497.52
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:29.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.08
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999984848

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.66
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000001636

Normal statistic for number of bits   :   0.013
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.12

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:43.38

 All tests were passed




Server wird beendet - Lösche Semaphor 117768214.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:10.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1258
p-value of test                       :    0.9981

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334378
  j =  1                              :        599997484
  j =  2                              :             1258
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:55.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:56.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:00.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:16.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:47.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.37
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   36.51
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.15
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.34
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.50
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6948.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.65
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:03.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.26
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.64
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5003.15
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:00.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45618
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869618
  j =  1                              :        399908770
  j =  2                              :            45606
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46142
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870142
  j =  1                              :        399907718
  j =  2                              :            46138
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  1.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:28.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.54e-3
p-value of test                       :    0.9921

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  5.8e-3

Anderson-Darling statistic = A2       :    5.33
p-value of test                       :  2.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  1.0e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:18.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:58.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:34.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.42e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.51e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:33.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.78
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:48.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.50
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.62
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.00
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.50
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17588.04
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.03
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.72
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.36
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.01
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.26
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.42
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.44
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.13
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.54
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.12
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.22
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.10
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.50
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.31
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.50
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.49
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.39
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.63
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.59
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.48
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.14
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.62
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.45
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.90
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.39
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.64
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.80
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.82
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.55
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.56
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:22.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.31
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   -1.40
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -2.01
p-value of test                       :    0.98

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.27e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 9.89e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.06
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.67
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.66
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:03.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.22
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:04.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.97
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10209.11
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:39.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.25
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.71
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.75
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4205.64
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11960.82
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.87
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000001120

Normal statistic for number of bits   : 8.85e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.16
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999982382

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  6.9e-3

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.47
p-value of test                       :  6.8e-3

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:03.34

 All tests were passed




Server wird beendet - Lösche Semaphor 118718486.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:54.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:06.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:07.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:00.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:05.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    2.24
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.37
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    2.87
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     639
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:15.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:45.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.25
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.51
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.81
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.67
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.05
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.52
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.99
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.08
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:07.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7156.79
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:53.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.85
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.65
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:09.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.17
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.70
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4950.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46006
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870006
  j =  1                              :        399907989
  j =  2                              :            46004
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45745
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869745
  j =  1                              :        399908518
  j =  2                              :            45729
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.25e-3
p-value of test                       :    0.9936

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:30.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:19.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:05.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-3
p-value of test                       :    0.9989

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.54
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.50e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.21e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:44.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:43.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.75
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.24
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.46
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.96
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.42
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.22
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.22
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17550.40
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.74
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.30
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.23
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.10
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.63
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.07
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.38
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.72
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.99
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.22
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.36
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.50
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.30
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.16
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.42
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.64
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.09
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.99
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.18
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.53
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.51
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.61
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.59
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.60
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.41
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.00
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.34
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.22
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.06
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.41
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:21.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.86e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.67e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.00
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.88
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.11
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:04.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.78
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9892.04
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9894.77
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.36
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:04:12.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.17
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4995.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:53.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3995.70
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4051.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11752.18
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12071.20
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.42
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000032911

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.20
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999957803

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:10.56

 All tests were passed




Server wird beendet - Lösche Semaphor 119734294.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5355
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:52.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:04.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:55.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:00.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.64
p-value of test                       :  4.4e-3

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:15.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:42.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.38
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.62
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.47
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.64
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.32
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.23
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.02
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  389.87
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.40
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:59.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7216.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:02.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.52
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.26
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4901.75
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:57.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46157
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870157
  j =  1                              :        399907691
  j =  2                              :            46147
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45704
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869704
  j =  1                              :        399908594
  j =  2                              :            45700
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-3
p-value of test                       :    0.9978

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:28.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:20.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:00.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.42e-4
p-value of test                       :  9.4e-3

Kolmogorov-Smirnov- statistic = D-    : 8.47e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:34.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.57
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:48.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.88
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.76
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.56
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.16
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.15
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:42.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.21
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.30
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.17
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17435.40
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.03
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.34
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.55
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.68
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.27
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.04
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.81
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.82
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.94
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.42
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.83
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.46
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.36
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.12
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.87
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.15
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.39
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.82
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.29
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.38
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.58
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.40
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:34.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.89
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.80
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.53
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.71
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.83
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.19
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:23.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.31
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9923

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.58e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.70e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.42
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.53
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.58
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:05.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.70
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10169.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.67
p-value of test                       :    0.9962

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:36.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.52
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:46.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.96
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:51.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.83
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4223.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12044.83
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11820.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.57
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999823982

Normal statistic for number of bits   :   -1.39
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.34
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999794810

Normal statistic for number of bits   :   -1.62
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.01
p-value of test                       :    0.98

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:09.23

 All tests were passed




Server wird beendet - Lösche Semaphor 120782870.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1469
p-value of test                       :  2.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334589
  j =  1                              :        599997062
  j =  2                              :             1469
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:55.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:43.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:59.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:11.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:11.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:15.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:14.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.14
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:45.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.59
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.93
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.14
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.33
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.59
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.43
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:29.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.43
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:58.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1514.24
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:05.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7157.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.08
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   91.77
p-value of test                       :  5.2e-3

-----------------------------------------------
CPU time used                    :  00:03:15.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.17
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:41.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5068.90
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:57.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45867
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869867
  j =  1                              :        399908270
  j =  2                              :            45859
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45918
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869918
  j =  1                              :        399908169
  j =  2                              :            45908
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.48e-3
p-value of test                       :    0.9917

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:28.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:18.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:04.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:52.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:45.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.16
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.06
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.19
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.45
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.52
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.29
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.39
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17703.98
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.62
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.36
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.05
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.57
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.22
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.47
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.49
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.81
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.01
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.28
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.93
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.69
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.61
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.97
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.76
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:40.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.43
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  196.69
p-value of test                       :  3.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.35
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.73
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.81
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.92
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.26
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.73
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.20
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.27
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.22
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.90
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.40
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.90
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.62
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.93
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    1.62
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:10.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.18
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :    2.63
p-value of test                       :  4.2e-3



-----------------------------------------------
CPU time used                    :  00:02:10.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    2.94
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.33
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.08
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.83
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:52.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.43
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:53.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.84
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:53.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5046.97
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.06
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4046.04
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.70
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.61
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.37
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000208924

Normal statistic for number of bits   :    1.65
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.39
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999862715

Normal statistic for number of bits   :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :  -0.100
p-value of test                       :    0.54

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:55.22

 All tests were passed




Server wird beendet - Lösche Semaphor 121765910.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5530
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:42.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:35.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:33.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:52.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:01.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:01.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:55.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:08.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.96
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.62
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.97
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.29
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.26
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.89
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.89
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.54
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.29
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:05.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7045.50
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.00
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.55
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:09.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.57
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.86
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:38.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5082.73
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:23.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46238
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870238
  j =  1                              :        399907525
  j =  2                              :            46236
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45655
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869655
  j =  1                              :        399908694
  j =  2                              :            45647
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:29.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:16.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 2.51e-3
p-value of test                       :    0.9974

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:57.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:53.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 9.53e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:43.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -3.37e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:44.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.85
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.76
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.74
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.93
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.34
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.84
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.51
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.10
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.91
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17637.60
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.31
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.63
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.81
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.62
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.60
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.03
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.86
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.17
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.43
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.29
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.52
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.38
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.63
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.16
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.53
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.66
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.42
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.05
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.94
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.50
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.72
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.61
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.29
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.53
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.50
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.23
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.39
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.78
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.32
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.69
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:25.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.88
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:25.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.05e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 3.68e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.84
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.88
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.62
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:06.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.88
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:08.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10202.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.51
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:04:21.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.83
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:54.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4255.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.09
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11824.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11709.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.83
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999982937

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.07
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000072868

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    2.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:11.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    2.38
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:16:19.19

 All tests were passed




Server wird beendet - Lösche Semaphor 101810183.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5426
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:47.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:37.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:36.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:55.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:02.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:02.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:52.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:57.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.81
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:14.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:44.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.61
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.54
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.68
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.23
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.67
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.93
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.39
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.75
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.02
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:00.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6945.15
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.82
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.97
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:03.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.39
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.17
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5108.01
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:11.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45671
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869671
  j =  1                              :        399908659
  j =  2                              :            45669
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46010
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870010
  j =  1                              :        399907983
  j =  2                              :            46004
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:27.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:17.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:58.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:54.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 8.99e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 9.36e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.38
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   99.93
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.07
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.01
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.93
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.54
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:41.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.09
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:30.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.01
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-3
p-value of test                       :    0.9912

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17748.51
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.04
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.28
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.27
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.12
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.73
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.41
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.03
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.22
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.69
p-value of test                       :    0.9911


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.13
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.63
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.83
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.12
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.31
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.57
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.95
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.07
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  579.84
p-value of test                       :  7.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.17
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.26
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.04
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5023.78
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.99
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  162.26
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.61
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.16
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.87
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.64
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.73
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.35
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:25.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.93
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:28.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 2.81e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.30
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.95
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.02
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:08.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.79
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.6e-3

Anderson-Darling statistic = A2       :    5.09
p-value of test                       :  2.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10386.05
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.044
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:39.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4732.15
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:48.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4780.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:49.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.84
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12011.53
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11599.15
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:30.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.73
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000088546

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.40
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000112882

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    2.36
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:58.13

 All tests were passed




Server wird beendet - Lösche Semaphor 103284743.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5323
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:50.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:39.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:58.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:08.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:08.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:04.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7508
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:04:12.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    3.75
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     834
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:14.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:43.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.16
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.59
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.40
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.00
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.45
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:59.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.32
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:10.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7376.66
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.34
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.35
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.62
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:41.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5112.64
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46163
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870163
  j =  1                              :        399907675
  j =  2                              :            46161
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45742
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869742
  j =  1                              :        399908522
  j =  2                              :            45730
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.10e-3
p-value of test                       :    0.9965

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.79
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:31.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  6.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.27
p-value of test                       :  6.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9979


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:20.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:54.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:11.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:57.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:40.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 9.33e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:24.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:54.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.30
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.55
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.32
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.17
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:49.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.01
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.6e-3

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17167.68
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.67
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.31
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.37
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.26
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.87
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.45
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.85
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.59
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.70
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.25
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.40
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.51
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.61
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.13
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.17
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.01
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.73
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.61
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.85
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.69
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.25
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.95
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4861.58
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.64
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.81
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.90
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.65
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.55
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.32
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.33
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.38
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   0.025
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:25.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.92
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:24.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   0.060
p-value of test                       :    0.48

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.67e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.61e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 6.25e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.37
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.19
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.42
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:06.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.36
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9951.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10019.42
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:04:37.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.70
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:58.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4236.62
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11862.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:36.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11655.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:37.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.21
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999980525

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   30.18
p-value of test                       :    0.9964


-----------------------------------------------
Total number of bits:  8000066778

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:14.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:58.85

 All tests were passed




Server wird beendet - Lösche Semaphor 104136711.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:09.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:07.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5437
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:49.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:38.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:36.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4221
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:54.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:04.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:05.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:58.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7057
p-value of test                       :    0.9989


-----------------------------------------------
CPU time used                    :  00:03:59.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     830
p-value of test                       :    0.9904

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     648
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:12.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.61
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.25
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.88
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.89
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.47
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1400.26
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7119.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.04
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.81
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:46.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.74
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5145.43
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9902


-----------------------------------------------
CPU time used                    :  00:02:57.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45913
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869913
  j =  1                              :        399908177
  j =  2                              :            45907
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45654
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869654
  j =  1                              :        399908694
  j =  2                              :            45650
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:26.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:19.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:54.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.30e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 6.36e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 8.06e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:42.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:41.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.15
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.78
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.80
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.77
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.97
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.59
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.11
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.37
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17325.00
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.24
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.97
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.42
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.82
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.67
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.40
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.65
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.72
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.07
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.74
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.09
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.26
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.81
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.74
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.87
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.81
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  563.72
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.42
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.23
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.08
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.36
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.99
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.83
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.95
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.60
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.59
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.06
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.92
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.08
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.38
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.23
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :    1.64
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:25.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.34e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 7.43e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 4.15e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.92
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.55
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.44
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.73
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:07.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10247.41
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10096.85
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.087
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.043
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:04:01.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 8.70e-3
p-value of test                       :    0.9906

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4687.35
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.13
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11938.43
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12025.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.70
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000009613

Normal statistic for number of bits   :   0.076
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.65
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999793496

Normal statistic for number of bits   :   -1.63
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:10.29

 All tests were passed




Server wird beendet - Lösche Semaphor 105512967.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:48.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:38.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:04.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:56.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:01.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    3.26
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     817
p-value of test                       :    0.9973

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9933

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.61
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9949

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:12.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:43.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.67
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.13
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.74
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.20
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.35
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.10
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.22
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:59.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7256.29
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:41.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.40
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:05.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.18
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.88
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4920.92
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:58.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908167
  j =  2                              :            45909
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45949
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869949
  j =  1                              :        399908107
  j =  2                              :            45939
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:27.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:44.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:00.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.95
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:34.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.16e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.74
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.58
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.30
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.74
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.12
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.61
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.21
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:44.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.39
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17482.35
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.51
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.34
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.01
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.80
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.15
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.56
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.86
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.02
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.77
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.10
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.86
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   92.79
p-value of test                       :    0.9983


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  108.06
p-value of test                       :  6.0e-3


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.23
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.89
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.19
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.15
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.89
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.60
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.98
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.47
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.20
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.37
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.66
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.63
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.86
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.76
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.37
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.53
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:24.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.05
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    1.81
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:25.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.00e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 6.04e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-2
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.88
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.57
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:06.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.46
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:08.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9894.65
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.07
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:42.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.05
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.63
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4227.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4372.62
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11681.28
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.73
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999813917

Normal statistic for number of bits   :   -1.47
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.69
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000150271

Normal statistic for number of bits   :    1.19
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         : -3.80e-3
p-value of test                       :    0.50

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9934

Tests on the sum of all N observations
Standardized normal statistic         :  -0.040
p-value of test                       :    0.52

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:14.43

 All tests were passed




Server wird beendet - Lösche Semaphor 106496007.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1471
p-value of test                       :  2.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334591
  j =  1                              :        599997058
  j =  2                              :             1471
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5406
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:48.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7479
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:39.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:05.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:05.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:56.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7548
p-value of test                       :  3.8e-3


-----------------------------------------------
CPU time used                    :  00:04:02.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:14.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    2.73
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.52
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.36
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.59
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.06
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.00
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.79
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.84
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1486.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7227.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.20
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.14
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:02.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.05
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.89
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:33.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5039.92
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:57.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908187
  j =  2                              :            45905
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45540
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869540
  j =  1                              :        399908923
  j =  2                              :            45534
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.41e-3
p-value of test                       :    0.9933

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:26.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:16.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.24e-3
p-value of test                       :    0.9917

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:33.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.59e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.97e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:35.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.53
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.16
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.96
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.60
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.35
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.01
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.05
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.52
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.20
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  166.90
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9940

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17446.89
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.39
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.64
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.38
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.80
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.29
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.96
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.40
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.53
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.99
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.98
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.49
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.09
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.37
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.86
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.69
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.26
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.74
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.43
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.60
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.20
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.39
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.78
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.31
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.58
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.03
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.06
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5139.20
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.47
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.72
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.82
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :   -1.87
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.39
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :   0.039
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:23.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.12
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.23
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.07
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.60
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.76
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:07.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:09.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.77
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10151.27
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:39.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:48.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.30
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:50.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.62
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.40
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11830.88
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.42
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999950567

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.51
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999987602

Normal statistic for number of bits   :  -0.098
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :  -0.093
p-value of test                       :    0.54

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.92
p-value of test                       :    0.03

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:18.70

 All tests were passed




Server wird beendet - Lösche Semaphor 107479047.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:48.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:38.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:38.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4137
p-value of test                       :    0.9988


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:04.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:04.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:55.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:00.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:45.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:11.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:42.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.97
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.61
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.69
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.30
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   88.56
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.66
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.38
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.59
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1475.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7065.06
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.61
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:03.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.31
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.55
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5097.30
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:06.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46002
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870002
  j =  1                              :        399908004
  j =  2                              :            45986
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46019
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870019
  j =  1                              :        399907965
  j =  2                              :            46013
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:26.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:18.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:58.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:53.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.15e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:34.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.50
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.72
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.97
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.65
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.26
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.87
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.61
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17773.93
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.52
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.63
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.20
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.84
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.70
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.81
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.23
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.24
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.88
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.59
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.40
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.48
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.66
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.54
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.69
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.73
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.17
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.43
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.51
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.89
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.94
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5112.86
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.57
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.13
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.51
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.74
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4887.68
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.07
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.95
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.25
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :   -1.25
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.62
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:22.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.65e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.98
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.58
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.33
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:06.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.78
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9749.88
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10019.24
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.017
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:42.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.99
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.24
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:50.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3923.62
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4194.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11786.67
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11889.58
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.50
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000036658

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.77
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999996428

Normal statistic for number of bits   :  -0.028
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:56.86

 All tests were passed




Server wird beendet - Lösche Semaphor 108462087.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5483
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:50.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4217
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:39.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:38.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:04.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:03.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:55.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:00.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9926


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     939
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    2.52
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:13.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.90
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.39
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.80
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.05
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.91
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.38
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:43.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.55
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:00.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6973.04
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.94
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.81
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:02.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.39
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.73
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4938.10
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:08.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46061
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870061
  j =  1                              :        399907881
  j =  2                              :            46055
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45703
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869703
  j =  1                              :        399908597
  j =  2                              :            45697
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:26.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:16.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:54.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.97e-3
p-value of test                       :    0.9907

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :  7.3e-4    *****

Anderson-Darling statistic = A2       :    8.16
p-value of test                       :  1.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:32.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.86e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.05e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.064
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.11
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:48.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.09
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.44
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:38.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.09
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.34
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.83
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.44
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17386.61
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.63
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.65
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.89
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.21
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.64
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.87
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.00
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   44.69
p-value of test                       :  9.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.11
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.08
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.77
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.73
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.51
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.57
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.88
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.54
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.23
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.47
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.35
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.29
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.81
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.43
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5116.71
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.38
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.21
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.93
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.49
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.97
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.09
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  158.51
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.86
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:24.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.94
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:25.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.44
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.19
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.61
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10188.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10044.58
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:44.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.36
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5068.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.73
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.57
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11838.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.75
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000119302

Normal statistic for number of bits   :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.83
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000111670

Normal statistic for number of bits   :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.69
p-value of test                       :    0.95

Sample variance                       :    2.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.97
p-value of test                       :  9.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.76
p-value of test                       :    0.9971

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:18.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 51  SampleProd, t = 16              1.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 109346823.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5392
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:53.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:54.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:00.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    2.31
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    2.57
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:13.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.28
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.78
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.16
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.12
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:59.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6905.96
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:41.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.55
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.67
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:02.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.12
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  166.52
p-value of test                       :  2.7e-3


-----------------------------------------------
CPU time used                    :  00:01:33.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5085.74
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:58.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45699
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869699
  j =  1                              :        399908607
  j =  2                              :            45689
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45930
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869930
  j =  1                              :        399908145
  j =  2                              :            45920
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:19.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:32.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 7.70e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.40
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:48.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.50
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   61.45
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:00:48.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.83
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.69
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.06
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.80
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17441.86
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.76
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.83
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.87
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.78
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.45
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.03
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.83
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.31
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.51
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.75
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.62
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.56
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.44
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.22
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.77
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.06
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.28
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.75
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.48
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.94
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.84
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.78
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.22
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.18
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.07
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.41
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.76
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.86
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:23.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.80
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.85e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.20
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.01
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.74
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:04.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.88
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:42.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.45
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.48
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.82
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11753.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12016.05
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.15
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000034777

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.86
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999954926

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.88
p-value of test                       :    0.03

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.33
p-value of test                       :    0.9902

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.73

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:01.10

 All tests were passed




Server wird beendet - Lösche Semaphor 110297095.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:50.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5523
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:52.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7164
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7529
p-value of test                       :  7.2e-3


-----------------------------------------------
CPU time used                    :  00:03:04.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7142
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:04.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:54.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:59.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:46.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.95
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:13.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.84
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.75
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.51
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.11
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.54
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.55
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.53
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.76
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  389.46
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:44.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.79
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6788.37
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.18
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:02.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.60
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.71
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4978.80
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:59.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45897
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869897
  j =  1                              :        399908208
  j =  2                              :            45893
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45743
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869743
  j =  1                              :        399908515
  j =  2                              :            45741
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:27.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:19.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:02.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:54.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:32.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 6.86e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.60e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 8.85e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.12
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.070
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:34.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.27
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.15
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.46
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.72
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.36
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.61
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.82
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.03
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17606.03
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.26
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.84
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.18
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.69
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.54
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.71
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.13
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.75
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.99
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.24
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.76
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  559.67
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.05
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.14
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.16
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.58
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.20
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.47
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.30
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.70
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  441.74
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  240.83
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.65
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.83
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.27
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.71
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.87
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.47
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:24.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.41
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:25.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 9.33e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.76e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.66
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.32
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.80
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.37
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:06.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.67
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 8.15e-3
p-value of test                       :    0.9912

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9704.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:40.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4777.85
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:48.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4985.46
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.81
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4046.35
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12067.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12084.93
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.68
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999865547

Normal statistic for number of bits   :   -1.06
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.42
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000116002

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:56.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 54  SampleMean, r = 10              0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 111280135.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5513
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:55.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:49.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:59.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:08.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:25.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:28.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:07.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:41.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.79
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:14.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:45.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.24
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.72
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.97
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.33
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.50
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  370.00
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:31.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1333.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:27.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7135.72
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.46
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.01
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:03.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.66
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.24
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5102.53
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:58.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45921
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869921
  j =  1                              :        399908165
  j =  2                              :            45907
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45795
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869795
  j =  1                              :        399908416
  j =  2                              :            45783
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:27.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:25.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:13.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:55.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:33.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.91e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.076
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:32.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.82
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.81
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.78
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.32
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:39.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.47
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.51
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17787.41
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.91
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.87
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.07
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.18
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.80
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.43
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.66
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.83
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.94
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.05
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.18
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.75
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.12
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.58
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.48
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.75
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.75
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.66
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.72
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.82
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.75
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.56
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.74
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  160.99
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.00
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.81
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5215.82
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.44
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.88
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.41
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:25.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.57
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.97e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.55
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.57
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.59
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:11.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:15.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9898.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9902.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5061.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.75
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4304.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.80
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.91
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.14
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.66
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000054265

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.18
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  8000050848

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   0.015
p-value of test                       :    0.49

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:51.04

 All tests were passed




Server wird beendet - Lösche Semaphor 112197639.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:55.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:57.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:04.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:05.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7143
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:58.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:00.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9946

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    2.07
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:11.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:41.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.23
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.30
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.60
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.61
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.62
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.14
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.25
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1376.79
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7092.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.43
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:09.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.88
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.67
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:37.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5046.14
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:56.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45891
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869891
  j =  1                              :        399908223
  j =  2                              :            45881
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45871
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869871
  j =  1                              :        399908263
  j =  2                              :            45861
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.10e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  7.8e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:30.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:19.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:02.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.072
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.39
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.17
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.62
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.95
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9983

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.16
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.17
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.24
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17442.61
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.61
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.53
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.40
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.98
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.01
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.93
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.01
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.09
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.67
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.33
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.21
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.41
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.82
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.56
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.16
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.02
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.94
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.09
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.30
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.50
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.33
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  324.91
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.86
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.89
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.75
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.96
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.31
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4828.34
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  318.20
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.74
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.36
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:22.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.39
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.59
p-value of test                       :  4.3e-4    *****

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    5.45
p-value of test                       :  1.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.51
p-value of test                       :    0.9939

Sample variance                       :    0.15
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 6.02e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.54
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.61
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.50
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:05.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:06.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9945.89
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.87
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:04:16.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5009.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:53.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4985.80
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:53.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.85
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.26
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11960.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12019.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:31.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.27
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999970952

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.96
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999920801

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    2.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:20.95

 All tests were passed




Server wird beendet - Lösche Semaphor 113115143.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5500
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:53.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7481
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:05.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:57.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7118
p-value of test                       :    0.9905


-----------------------------------------------
CPU time used                    :  00:03:59.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    4.52
p-value of test                       :  4.9e-3

-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.42
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    2.55
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     268
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:13.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:42.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.44
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.43
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.33
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.81
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.21
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.64
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.64
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7192.42
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.96
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.01
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:08.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.27
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4946.41
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:57.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45667
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869667
  j =  1                              :        399908670
  j =  2                              :            45659
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46042
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870042
  j =  1                              :        399907916
  j =  2                              :            46042
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:30.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:18.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:57.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 5.20e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.74e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.93e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.030
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.078
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:42.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.86
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.83
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.70
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.93
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:45.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.28
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.50
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17579.58
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.23
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.90
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.42
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.63
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.24
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.87
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.05
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.54
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.25
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.05
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.99
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.08
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.99
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.66
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.15
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.36
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.43
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.12
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.74
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.16
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.22
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.15
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.99
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.49
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4915.81
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.11
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.35
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.01
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:21.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.96
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.33
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.81
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.40
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:06.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    5.09
p-value of test                       :  2.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  145.53
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:02:05.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.15
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10148.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.34
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:04:14.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5004.37
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:52.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.89
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:54.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.72
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4226.05
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11720.04
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.54
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.72
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999911492

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.77
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999906437

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.19
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:05.64

 All tests were passed




Server wird beendet - Lösche Semaphor 114163719.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1489
p-value of test                       :  4.5e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334609
  j =  1                              :        599997022
  j =  2                              :             1489
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5357
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:54.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4464
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7144
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:03.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:53.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:59.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:45.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.78
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    2.33
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:13.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:43.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.24
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.76
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.71
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.86
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.54
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.08
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.32
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.60
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.33
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7069.28
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.36
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.48
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:03.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.51
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.69
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4855.40
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:57.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45555
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869555
  j =  1                              :        399908893
  j =  2                              :            45549
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45676
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869676
  j =  1                              :        399908651
  j =  2                              :            45670
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:27.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:18.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:59.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:34.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:35.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.52
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.69
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.62
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:37.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.60
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.72
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.91
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.8e-3

Anderson-Darling statistic = A2       :    3.50
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17805.70
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.01
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.90
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.85
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.55
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.04
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.04
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.76
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.93
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.19
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.81
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.47
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.58
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.59
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.06
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.35
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.00
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.14
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.07
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.67
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.50
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.08
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.88
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5143.15
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.56
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.88
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  315.19
p-value of test                       :    0.9957


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.96
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.35
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.38
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.27
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.04
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :  -0.046
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:21.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.97
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:23.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 9.83e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.01e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.67
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.86
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.90
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:06.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.70
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:05.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9828.42
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.43
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:40.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.81
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.00
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:49.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.91
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4245.05
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.93
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12076.21
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.04
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999971411

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.77
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999928892

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.27

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:04.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  4  CollisionOver, t = 2            4.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 115245063.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1254
p-value of test                       :    0.9987

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334374
  j =  1                              :        599997492
  j =  2                              :             1254
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5441
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:56.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:05.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:04.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:55.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:59.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    2.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:13.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.87
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    4.69
p-value of test                       :  4.1e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     182
p-value of test                       :  6.2e-3

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:39.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.36
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.57
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.42
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.30
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.64
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.43
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  514.57
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:01:45.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6929.66
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.16
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:05.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.48
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.76
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5135.27
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:55.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45783
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869783
  j =  1                              :        399908436
  j =  2                              :            45779
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46050
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870050
  j =  1                              :        399907906
  j =  2                              :            46038
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:27.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:17.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:55.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:32.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 2.82e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:35.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:37.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.65
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.66
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.16
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.31
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.34
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.64e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  161.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17065.05
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.68
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   61.46
p-value of test                       :  3.7e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.78
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.58
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.25
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.94
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.98
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.85
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.91
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.22
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.91
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.89
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.13
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.57
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.06
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.58
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.99
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.80
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.12
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.35
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.32
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.07
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.56
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.12
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.73
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.54
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4800.40
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.14
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.23
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.83
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :   -1.64
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.97
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:21.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 8.18e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.21e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 6.22e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.11
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.91
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.95
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:05.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.86
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9835.77
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:38.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5059.51
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.83
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:51.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3964.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4247.21
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11871.69
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:29.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.20
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000168694

Normal statistic for number of bits   :    1.33
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.53
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000052549

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.32

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.18
p-value of test                       :    0.99

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:05.31

 All tests were passed




Server wird beendet - Lösche Semaphor 116260871.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5329
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7121
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:41.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4518
p-value of test                       :  3.2e-3


-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:07.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:05.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:56.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:58.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    2.48
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.95
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    2.22
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:16.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:47.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.95
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.60
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.49
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.40
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.67
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.02
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.97
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.16
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:03.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7161.26
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.01
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:05.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.16
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:46.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.15
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:36.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5100.66
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45921
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869921
  j =  1                              :        399908163
  j =  2                              :            45911
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45751
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869751
  j =  1                              :        399908503
  j =  2                              :            45741
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:28.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:20.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:44.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.80e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:37.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:37.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.78
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.23
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.98
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.39
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.78
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:45.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.62
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.09
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.00
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.83e-3
p-value of test                       :    0.9927

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   98.36
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17290.80
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.10
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.02
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.87
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.18
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.32
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.55
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.56
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.05
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.57
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.89
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.40
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.83
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.57
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.42
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.12
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.78
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.27
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.87
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.46
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.98
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.57
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.43
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.36
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.34
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.14
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.43
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  154.45
p-value of test                       :    0.9927


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.39
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:22.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.32
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -2.44
p-value of test                       :    0.9927



-----------------------------------------------
CPU time used                    :  00:02:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.86e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 7.76e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.71
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.74
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.46
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.75
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.10
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10226.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:52.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.74
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:56.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4203.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.13
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.76
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:32.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11908.43
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.09
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000148759

Normal statistic for number of bits   :    1.18
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.92
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999922628

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:17.67

 All tests were passed




Server wird beendet - Lösche Semaphor 117276679.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1262
p-value of test                       :    0.9973

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334382
  j =  1                              :        599997476
  j =  2                              :             1262
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5447
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:57.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:57.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:05.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7492
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:55.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:01.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    2.53
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     984
p-value of test                       :  3.0e-3

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:16.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:46.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.50
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.39
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.56
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.53
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.04
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1340.17
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6983.77
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.55
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.91
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:03.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.94
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.00
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:34.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5065.72
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:10.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46087
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870087
  j =  1                              :        399907828
  j =  2                              :            46083
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46215
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870215
  j =  1                              :        399907571
  j =  2                              :            46213
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:28.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:18.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  9.5e-3

Anderson-Darling statistic = A2       :    3.96
p-value of test                       :  9.3e-3


-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:55.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.67e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 9.34e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.91
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:47.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.24
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.48
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.97
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.77
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.27
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.96
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.32
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.35
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.099
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.66
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17404.60
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.78
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.06
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.17
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.77
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   59.10
p-value of test                       :  9.0e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.98
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.31
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.00
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.17
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.29
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.49
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.06
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.15
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.39
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.22
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.64
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.94
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.04
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.05
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.09
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.13
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5108.53
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.86
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.23
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.93
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.25
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.97
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.56
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.37
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.36
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:21.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.56
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.76e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.29e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 8.84e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.41
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.05
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.38
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:15.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.26
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:06.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10022.93
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10173.17
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.46
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:37.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4717.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.63
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:50.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.29
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12143.78
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11660.67
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.76
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999955244

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.52
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000069130

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :  -0.049
p-value of test                       :    0.52

Sample variance                       :    1.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:09.34

 All tests were passed




Server wird beendet - Lösche Semaphor 118259719.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1514
p-value of test                       :  3.5e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334634
  j =  1                              :        599996972
  j =  2                              :             1514
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5343
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:56.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:05.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:05.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:54.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:00.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    3.13
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:16.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    2.28
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:48.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.86
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.80
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.24
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.29
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.70
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.70
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1501.73
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:01.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6956.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:43.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.33
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:05.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.89
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.07
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:32.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5137.82
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:05.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45815
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869815
  j =  1                              :        399908371
  j =  2                              :            45813
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45846
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869846
  j =  1                              :        399908310
  j =  2                              :            45842
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:27.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:17.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 2.62e-3
p-value of test                       :    0.9972

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:45.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:59.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:54.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:32.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.37e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.74e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:37.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:47.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.20
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:48.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.91
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.84
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   13.00
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.37
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.63
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.74
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17302.41
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.67
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.17
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.75
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.98
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.76
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.51
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.98
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.12
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.42
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.81
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.27
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.90
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  100.78
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.94
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.16
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.40
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.74
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.59
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.26
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.52
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.65
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.27
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.54
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.40
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.93
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.64
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.36
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.18
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.83
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:21.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.12
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:24.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 7.60e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 5.54e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.51
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.15
p-value of test                       :    0.9971

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.50
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:06.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.25
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:05.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10110.96
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10067.13
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.076
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:37.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.54
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5022.84
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:51.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4239.41
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11727.49
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.79
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.42
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000057571

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.22
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999986786

Normal statistic for number of bits   :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.83

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9910

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:24.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           3.5e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 119275527.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5502
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:58.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:06.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:06.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:55.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:00.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.82
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    2.24
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:12.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     125
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    3.43
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:47.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.21
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.94
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.16
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.12
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.56
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.94
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.29
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.42
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.13
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1349.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:02.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7020.72
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.17
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.52e-3
p-value of test                       :    0.9942

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.68
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:05.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.90
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.80
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4952.31
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:01.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46089
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870089
  j =  1                              :        399907827
  j =  2                              :            46079
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45674
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869674
  j =  1                              :        399908656
  j =  2                              :            45666
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:28.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:19.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:59.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:54.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:33.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.01e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.90e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.88
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:01:33.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.77
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:48.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.44
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.41
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.60
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.48
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.16
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.70
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.26
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.80
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17600.22
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.86
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.09
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.20
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.33
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.71
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.43
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.25
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.74
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   44.80
p-value of test                       :  6.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.12
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.92
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.10
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.92
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.25
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.88
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.57
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.21
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.10
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.13
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.26
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.82
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.78
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4867.41
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.89
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.89
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.64
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.24
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.42
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.03
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.62
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   -1.71
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:22.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.93
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   -1.58
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 5.27e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.96e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 5.98e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.82
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.14
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.27
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:04.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.12
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:05.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9627.19
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10121.08
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:40.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4724.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.58
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:51.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.01
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11760.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12150.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.23
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999970982

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   86.55
p-value of test                       :  3.2e-3


-----------------------------------------------
Total number of bits:  8000018880

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :  -0.049
p-value of test                       :    0.52

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.30
p-value of test                       :    0.99

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.00
p-value of test                       :    0.98

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:57.11

 All tests were passed




Server wird beendet - Lösche Semaphor 120258567.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:59.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:42.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:58.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:08.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:08.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:59.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:02.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.11
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    2.25
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.46
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:14.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:41.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.60
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.51
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.32
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.04
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.29
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1512.97
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:04.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7149.91
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.80
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:07.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.91
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.60
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5160.58
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:02.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45884
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869884
  j =  1                              :        399908234
  j =  2                              :            45880
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46032
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870032
  j =  1                              :        399907940
  j =  2                              :            46024
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:31.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:19.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:35.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.86e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:44.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:44.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.22
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.25
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.31
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.89
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.27
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.32
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:40.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17523.81
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.38
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.51
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.01
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.58
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.28
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.36
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.00
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.54
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.25
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.12
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.80
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.24
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.14
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.18
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.27
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.35
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.49
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.34
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.38
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.06
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.66
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.79
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.06
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.93
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5142.86
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  322.60
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.88
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.08
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:20.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.26
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:21.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.11
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.18
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.67
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.77
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:02.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.52
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:01.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.62
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.61
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:45.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.15
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:45.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4194.95
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.38
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11797.90
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11993.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.15
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999986936

Normal statistic for number of bits   :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.75
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999960956

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-5
p-value of test                       : 1 -  1.9e-5    *****

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.6e-3

Anderson-Darling statistic = A2       :    3.75
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.79
p-value of test                       :  2.6e-3

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:52.55

 All tests were passed




Server wird beendet - Lösche Semaphor 121241607.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5409
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:45.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4451
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:38.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:47.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:10.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:28.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:29.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:09.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:48.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    3.04
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.03
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:08.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.36
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:36.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.24
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.45
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.59
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.21
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.73
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.22
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.60
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.27
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:47.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.16
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:05.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7183.00
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.12
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.63
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:13.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.63
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:46.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.20
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:39.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5136.73
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:20.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46352
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870352
  j =  1                              :        399907303
  j =  2                              :            46338
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45850
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869850
  j =  1                              :        399908305
  j =  2                              :            45840
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:38.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:02.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:18.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:53.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.21
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.76
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.43
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.93
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.15
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.22
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.38
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.95
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.83e-3
p-value of test                       :    0.9960

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   95.91
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17715.34
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.65
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.90
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.60
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.66
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.83
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.84
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.65
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.48
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.88
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.44
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.33
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.08
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.20
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.07
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.15
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.62
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.58
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.60
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.49
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.52
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.02
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.51
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.31
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.03
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.00
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.37
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.67
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.78
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -1.87
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:23.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.30
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    1.44
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:26.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 4.93e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 3.82e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.28
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.62
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.84
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.47
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:07.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.95
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9849.04
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.046
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : 4.28e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:04:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.40
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:53.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5027.31
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:56.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4229.98
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.62
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.41
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:36.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11605.73
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:34.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.17
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000024607

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.25
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999952274

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.16
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:21:56.17

 All tests were passed




Server wird beendet - Lösche Semaphor 101842952.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5284
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:47.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:38.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:36.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:02.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:02.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:52.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:00.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9921


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    3.12
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     269
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:15.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.74
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     175
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:43.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.18
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.23
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.86
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.73
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.03
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.29
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:53.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.62
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7103.05
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.27
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.87
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.91
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:35.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4859.42
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:58.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45911
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869911
  j =  1                              :        399908182
  j =  2                              :            45903
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45703
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869703
  j =  1                              :        399908597
  j =  2                              :            45697
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:25.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:16.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:44.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.03
p-value of test                       :  8.5e-3

-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:32.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.77e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.11e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 8.31e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.071
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:34.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:35.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.66
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.12
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.39
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.49
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.43
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:44.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.42
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.17
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.89
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17262.08
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.71
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.39
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.24
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.91
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.53
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.68
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.91
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.87
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.37
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.88
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.32
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.86
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.49
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.12
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.19
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.72
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.59
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.16
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.58
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  445.04
p-value of test                       :  9.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  246.33
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.65
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.78
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.07
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.04
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.12
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.31
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    1.32
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:26.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.07
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:24.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 2.31e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.93e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 4.70e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.21
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.23
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.26
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:07.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.16
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:08.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10067.67
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10120.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.091
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.095
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:42.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.97
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    6.11
p-value of test                       :  9.4e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5221.51
p-value of test                       :  5.1e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:50.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4007.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11847.82
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.01
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.34
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000088141

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.88
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999992795

Normal statistic for number of bits   :  -0.057
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9995    *****

Tests on the sum of all N observations
Standardized normal statistic         :   0.095
p-value of test                       :    0.46

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:30.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 96  HammingIndep, L=30, r=27        5.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 103350280.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:47.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4231
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:38.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7060
p-value of test                       :    0.9988


-----------------------------------------------
CPU time used                    :  00:02:36.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:02.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:02.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:52.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:01.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:13.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.57
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:45.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.11
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.63
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.52
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:47.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.27
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6992.50
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:02.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.70
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.36
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5026.08
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:03.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45768
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869768
  j =  1                              :        399908467
  j =  2                              :            45762
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45714
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869714
  j =  1                              :        399908575
  j =  2                              :            45708
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :  3.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    4.87
p-value of test                       :  3.3e-3


-----------------------------------------------
CPU time used                    :  00:02:27.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:18.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:33.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 6.28e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:34.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.78
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.74
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.83
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.91
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.75
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.41
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:42.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.72
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.47
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17294.96
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.70
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.25
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.05
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.34
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.11
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.16
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.35
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.17
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.69
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.32
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.02
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.59
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.34
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.65
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.56
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.87
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.03
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.32
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.28
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4866.01
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.05
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  155.91
p-value of test                       :    0.9908


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.07
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.48
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.14
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.10
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.84
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.84
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:24.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.74
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    2.32
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:02:26.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 7.36e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.25e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.85
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.99
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.77e-4
p-value of test                       :    0.9994    *****

Anderson-Darling statistic = A2       :    4.48
p-value of test                       :  5.3e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  145.48
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:02:09.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.74
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:08.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9736.20
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.02
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:41.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5001.93
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4997.84
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.56
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11677.80
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11835.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.66
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000159148

Normal statistic for number of bits   :    1.26
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.30
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999820472

Normal statistic for number of bits   :   -1.42
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :  -0.059
p-value of test                       :    0.52

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:27.65

 All tests were passed




Server wird beendet - Lösche Semaphor 104267784.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:42.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5365
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:47.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:38.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:37.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:01.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:01.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:52.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7484
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:59.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:45.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:12.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9912


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.88
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.85
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.64
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.12
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.85
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.56
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7078.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.55
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   38.35
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:03.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.56
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.30
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:34.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5006.67
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:58.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46103
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870103
  j =  1                              :        399907798
  j =  2                              :            46095
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46016
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870016
  j =  1                              :        399907972
  j =  2                              :            46008
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
p-value of test                       :    0.9917

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:27.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:16.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :  1.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.43
p-value of test                       :  5.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9963


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:01.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:32.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 2.23e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:30.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:32.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.99
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.96
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.65
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.23
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.94
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.70
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  2.1e-3

Kolmogorov-Smirnov- statistic = D-    : 8.87e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    5.02
p-value of test                       :  3.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   18.94
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.11
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17495.10
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.56
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.69
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.02
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.79
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.66
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.98
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.24
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.09
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.91
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.41
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.89
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.89
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.25
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.24
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.44
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.78
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.09
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.45
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.03
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.29
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.44
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.63
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.65
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.11
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.80
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.62
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.74
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.16
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.61
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:25.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.54
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -1.50
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 5.09e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.16e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.96
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.35
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:07.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.09
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:07.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9845.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.30
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:42.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4775.13
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:50.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4198.77
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.11
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.62
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12160.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:29.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.78
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999941075

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.20
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000062584

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   0.078
p-value of test                       :    0.47

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:37.09

 All tests were passed




Server wird beendet - Lösche Semaphor 105185288.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:48.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:38.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7174
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:37.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:54.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:03.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:01.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:52.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:59.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:44.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    3.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:12.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:43.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.13
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.47
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.30
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  472.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6865.89
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:01.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.82
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.91
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:34.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4987.03
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:59.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45418
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869418
  j =  1                              :        399909169
  j =  2                              :            45408
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46092
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870092
  j =  1                              :        399907819
  j =  2                              :            46086
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:27.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:17.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:32.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.87e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 3.58e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.062
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:33.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.27
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:47.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.41
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.20
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.32
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.41
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.07
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.39
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.27
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.6e-3

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17712.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.02
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.93
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.84
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.76
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.79
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.01
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.88
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.45
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.48
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.41
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.10
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.87
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.92
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.30
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.88
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.48
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.90
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.15
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.92
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.97
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.19
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.30
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.54
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  241.06
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.23
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.02
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5105.05
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.59
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.55
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.05
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :    1.33
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.37
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:22.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    4.73
p-value of test                       :  4.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.61
p-value of test                       :    0.9955

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.82e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 7.27e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.42e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.11
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.89
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.54
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:08.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.89
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:07.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9865.99
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:42.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:50.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.45
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4369.26
p-value of test                       :  3.1e-3

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11995.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.22
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.24
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999894254

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.05
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000223264

Normal statistic for number of bits   :    1.77
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  2.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.93
p-value of test                       :  9.8e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.63
p-value of test                       :    0.9957

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:26.96

 All tests were passed




Server wird beendet - Lösche Semaphor 106070024.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:40.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5392
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:48.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:39.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:38.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:08.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:57.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:04.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:13.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.84
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:42.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.68
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.09
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.34
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.92
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.54
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.42
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.00
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:08.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6947.27
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:57.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.87
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:18.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.55
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.08
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5040.48
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45837
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869837
  j =  1                              :        399908331
  j =  2                              :            45827
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46017
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870017
  j =  1                              :        399907971
  j =  2                              :            46007
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:32.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:08.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.04e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 3.60e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:24.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:49.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  103.38
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.83
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.81
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.05
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.57
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17515.07
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.76
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.21
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.38
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.78
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.86
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.49
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.08
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.57
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.81
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.85
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.66
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.97
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.60
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.15
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.90
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.64
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.85
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.27
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  100.14
p-value of test                       :    0.9909


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.98
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.22
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.21
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4877.03
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.95
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  162.46
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.11
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.76
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.20
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.81
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.11
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.11
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.45
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -1.57
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:23.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 8.94e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.03
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.96
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.59
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10131.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.04
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.074
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:04:29.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.58
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.99
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:59.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3972.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.49
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11645.78
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.01
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000085696

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.91
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000033205

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :  -0.081
p-value of test                       :    0.53

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:10.56

 All tests were passed




Server wird beendet - Lösche Semaphor 107020296.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:40.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5406
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:49.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:39.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:37.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4467
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:05.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:05.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:58.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:01.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:13.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.22
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.56
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.74
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.78
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.44
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1350.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:04.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6968.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.85
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:08.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.31
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.81
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:37.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5178.76
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:01.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45846
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869846
  j =  1                              :        399908311
  j =  2                              :            45840
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46334
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870334
  j =  1                              :        399907335
  j =  2                              :            46328
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:29.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:17.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :  8.9e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    4.36
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:01:55.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:36.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.39e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.83
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:01:43.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.07
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.29
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.89
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.81
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.52
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:46.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.60
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.94
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.52
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17283.05
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.01
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.34
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.74
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.07
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.03
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.52
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.17
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.93
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.69
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.47
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.46
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.82
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.78
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.16
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.73
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.97
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.84
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.59
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.49
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.56
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4770.37
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.63
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.30
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.26
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.47
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.21
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.23
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.47
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.50
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:22.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.77
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :    1.32
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:23.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.83e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.23e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 4.75e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.59
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.89
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.07e-3
p-value of test                       :    0.9925

Anderson-Darling statistic = A2       :    5.84
p-value of test                       :  1.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  140.40
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:02:06.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10249.29
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10124.12
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:04:13.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5108.85
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:53.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5059.91
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:53.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.17
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11850.64
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:30.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.96
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000037876

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.37
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000188974

Normal statistic for number of bits   :    1.49
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:11.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9929

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:46.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 89  PeriodsInStrings, r = 20        0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 108265480.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:50.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:39.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:04.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:05.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:58.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:01.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9940

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:13.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:41.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.35
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.84
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.83
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.79
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.27
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.65
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.25
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7084.79
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  2.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.97
p-value of test                       :  9.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   35.04
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.97
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.12
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5021.25
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:55.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45669
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869669
  j =  1                              :        399908664
  j =  2                              :            45665
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46079
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870079
  j =  1                              :        399907844
  j =  2                              :            46075
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:27.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:15.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:36.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.61e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.034
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:43.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.38
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.85
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.83
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.97
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.05
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.57
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:46.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.21
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.57
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17350.47
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.11
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.44
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.06
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.96
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.75
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.61
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.59
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.90
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.07
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.80
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.78
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.82
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.10
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.74
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.29
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.64
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.75
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.28
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.22
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.37
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.85
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.38
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.70
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.61
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.63
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.97
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.17
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :    1.99
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:24.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.30
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:24.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 2.52e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.05e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 5.29e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.52
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.40
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9942

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.32
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.87
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:06.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9858.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.86
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:04:14.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5025.12
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:53.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4981.78
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:55.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4221.24
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.60
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.93
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:30.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11900.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.91
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000015352

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.04
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000021292

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.44
p-value of test                       :    0.08

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:47.02

 All tests were passed




Server wird beendet - Lösche Semaphor 109379592.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5549
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:53.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:43.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4183
p-value of test                       :    0.9903


-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:01.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:09.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:14.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.07
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:14.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.99
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:42.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.98
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.26
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.89
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.89
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.11
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.73
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.51
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.70
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:04.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7128.68
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.30
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.89
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.47
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.17
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:43.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5037.83
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:54.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45902
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869902
  j =  1                              :        399908198
  j =  2                              :            45898
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45584
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869584
  j =  1                              :        399908834
  j =  2                              :            45580
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:31.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:21.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  8.8e-3

Anderson-Darling statistic = A2       :    4.24
p-value of test                       :  6.8e-3


-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:12.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:58.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:39.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:51.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:52.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.34
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.81
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.30
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.73
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.90
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:50.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.33
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.64
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.094
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.35
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17288.32
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.69
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.37
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.43
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.74
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.80
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.92
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.96
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.72
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.48
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.75
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.57
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.69
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.48
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.05
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.23
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.44
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.86
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.07
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.52
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.09
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.39
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4879.09
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.08
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.87
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.92
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.34
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4816.86
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.10
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.08
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.42
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.52
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:23.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.26e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.15
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.24
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.75
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:11.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.50
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:12.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.46
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:04:31.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4751.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:54.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4984.13
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:58.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4253.16
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4007.78
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11571.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12187.54
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.94
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000096898

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.23
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000023389

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   0.063
p-value of test                       :    0.47

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.9e-3

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:00.03

 All tests were passed




Server wird beendet - Lösche Semaphor 110493704.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.99

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:54.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:05.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:05.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:56.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:01.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.78
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:13.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.00
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:46.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.08
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.80
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.05
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.30
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:43.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1347.48
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6977.85
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:41.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.58
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.52
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.32
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.29
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:33.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5015.17
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:58.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45947
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869947
  j =  1                              :        399908108
  j =  2                              :            45943
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45751
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869751
  j =  1                              :        399908502
  j =  2                              :            45743
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:28.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:00.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:35.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.13e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.25e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:40.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.04
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.57
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.94
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.86
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.74
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.41
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 8.39e-3
p-value of test                       :    0.9910

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17093.13
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.75
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.06
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.61
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.53
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.69
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.32
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.11
p-value of test                       :    0.9941


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.02
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.18
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.46
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.29
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.03
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.01
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.58
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.50
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  414.55
p-value of test                       :    0.9978


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.66
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.74
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.78
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.31
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.82
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.93
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  137.89
p-value of test                       :    0.9997    *****


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.14
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.01
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.96
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.90
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.49
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.12
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -1.54
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:23.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.44
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.98e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.10
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.66
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.35
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:06.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.53
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.79
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9786.12
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.54
p-value of test                       :    0.9945

-----------------------------------------------
CPU time used                    :  00:03:37.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :  8.0e-4    *****

Anderson-Darling statistic = A2       :    5.83
p-value of test                       :  1.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5217.74
p-value of test                       :  5.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:45.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.08
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.26
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.37
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.21
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000076912

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.90
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000133423

Normal statistic for number of bits   :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.075
p-value of test                       :    0.47

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:31.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 C (L=10000, r=0)    0.9997 
 95  HammingIndep, L=30, r=0         5.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 111575048.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1264
p-value of test                       :    0.9968

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334384
  j =  1                              :        599997472
  j =  2                              :             1264
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5371
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:54.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:04.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:05.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:56.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:01.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     842
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.48
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    3.53
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.50
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:13.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:44.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.09
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.27
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.83
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.37
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.03
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:43.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6994.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:41.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.53
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.34
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:03.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.53
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.97
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:32.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5064.41
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:57.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45984
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869984
  j =  1                              :        399908035
  j =  2                              :            45978
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45917
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869917
  j =  1                              :        399908166
  j =  2                              :            45917
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:18.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:33.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 7.29e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.71e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 3.47e-4
p-value of test                       :  8.2e-3

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.38
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.036
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:39.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.01
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.60
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.98
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.12
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.55
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17611.15
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.30
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.04
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.53
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.51
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.88
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.14
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.49
p-value of test                       :    0.9902


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.81
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.39
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.57
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.84
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.11
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.23
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.61
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.48
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.14
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.01
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.06
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.31
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.58
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.08
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.13
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.45
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.61
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.14
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.73
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.82
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.24
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.02
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.94
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:24.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.86
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:23.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.70
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.45
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.87
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:04.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.18
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:05.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10082.23
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10241.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:39.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.91
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.56
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.58
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11900.02
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12026.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.27
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000046126

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.17
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999962978

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:04.15

 All tests were passed




Server wird beendet - Lösche Semaphor 112590856.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:16.37

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:02.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:53.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:05.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:56.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:01.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    2.26
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     659
p-value of test                       :  9.2e-3

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    3.03
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:13.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:41.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.36
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.25
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.03
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1400.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7029.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:41.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.70
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.19
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:04.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.23
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.17
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4925.98
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:59.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46009
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870009
  j =  1                              :        399907984
  j =  2                              :            46005
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46026
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870026
  j =  1                              :        399907952
  j =  2                              :            46018
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:27.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:19.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :  1.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    7.14
p-value of test                       :  3.0e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9997    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:35.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.88e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.075
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:35.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:38.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.61
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.37
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.63
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.84
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.91
p-value of test                       :  1.0e-2

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.05
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.02
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.89
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.77
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17490.44
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.44
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.18
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.69
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.00
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.94
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.50
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.01
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.16
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.16
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.35
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.49
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.20
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.56
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.27
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.99
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.97
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.44
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.26
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.92
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.52
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.51
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5150.46
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.08
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.98
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.93
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  317.25
p-value of test                       :    0.9945


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.81
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.33
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.16
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.74
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.62
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:21.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.66e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 8.99e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   22.35
p-value of test                       :  4.3e-3

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.61
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.39
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:04.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.94
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10193.79
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10127.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:40.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4974.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:47.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.81
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.57
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.14
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11729.88
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11927.48
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.22
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999951401

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.97
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000212122

Normal statistic for number of bits   :    1.68
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:46.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 49  MaxOft, t = 32                  0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 113606664.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:52.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:39.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:55.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:57.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:04.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:05.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:56.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:01.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.47
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:47.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:13.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.11
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    2.03
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     175
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   23.03
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.30
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.66
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.64
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.89
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.11
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.88
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7204.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.12
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.15
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:03.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.83
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.14
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:33.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5036.51
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:59.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45948
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869948
  j =  1                              :        399908112
  j =  2                              :            45932
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45677
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869677
  j =  1                              :        399908647
  j =  2                              :            45675
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:28.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:17.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:00.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:32.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.44e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:27.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.064
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.14
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.64
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.05
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.55
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:45.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.71
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.01
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.46
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.38
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.62
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17645.45
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.27
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.97
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.48
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.78
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.12
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.47
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.62
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.28
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.53
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.66
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.26
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.49
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.62
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.52
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.08
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.74
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.67
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.40
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.88
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:47.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.29
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.07
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.19
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.61
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.25
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.51
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.46
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4817.59
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.79
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.28
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.23
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:23.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.67
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.92e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 8.23e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.40
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.57
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.88
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:04.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.18
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:05.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.04
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.52
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.054
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:39.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5009.30
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4814.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4251.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.67
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11675.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11961.52
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.62
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999968117

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.94
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999876155

Normal statistic for number of bits   :   -0.98
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   0.050
p-value of test                       :    0.48

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:16.62

 All tests were passed




Server wird beendet - Lösche Semaphor 114622472.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1235
p-value of test                       :    0.9998    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334355
  j =  1                              :        599997530
  j =  2                              :             1235
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5329
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:51.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:38.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4211
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:04.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:04.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:01.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.44
p-value of test                       :  1.8e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     329
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:12.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.58
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.61
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:44.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.65
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.50
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.53
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  379.97
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1543.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6951.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:23.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.32
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.71
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4846.94
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:59.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46123
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870123
  j =  1                              :        399907757
  j =  2                              :            46117
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46054
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870054
  j =  1                              :        399907899
  j =  2                              :            46040
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:28.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:18.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:00.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:34.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.59e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:24.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.47e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:26.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:36.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.56
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.14
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.06
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.61
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.06
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.28
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.70
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.41
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.76
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.27
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17599.95
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.92
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.14
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.73
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.21
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.78
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.07
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.03
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.34
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.13
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.68
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.91
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.72
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.24
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.26
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.86
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.33
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.47
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.44
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.37
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.90
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.22
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.90
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4872.82
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.01
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.16
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.55
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.03
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.25
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.23
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.80
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :   -2.44
p-value of test                       :    0.9926



-----------------------------------------------
CPU time used                    :  00:02:21.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.97
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -1.57
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.49e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.17e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.59
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.97
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.18
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:05.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.17
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:05.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.93
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.71e-3
p-value of test                       :    0.9906

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10249.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:38.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.97
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:50.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.38
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4248.84
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11764.41
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.05
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.66
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999932417

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.03
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999939119

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:25.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 115539976.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.49

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5413
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:52.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4224
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:38.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4213
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:05.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7136
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:07.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:01.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:03.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.82
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    2.95
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:13.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:42.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.74
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.09
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.58
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.27
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.22
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.91
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:51.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.47
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:08.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7050.28
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.74
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   39.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:09.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.11
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.65
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4771.95
p-value of test                       :    0.9966


-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:07.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46037
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870037
  j =  1                              :        399907930
  j =  2                              :            46029
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45293
p-value of test                       :    0.9969


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869293
  j =  1                              :        399909420
  j =  2                              :            45281
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:30.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:02.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.69
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.26
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.99
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.62
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.80
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.35
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17500.07
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.61
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.56
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.80
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.77
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.77
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.01
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.54
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.74
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.40
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.85
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.81
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.81
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  422.21
p-value of test                       :    0.9950


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.90
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.23
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  102.69
p-value of test                       :    0.9974


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.38
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.47
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.65
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.42
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.51
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.59
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.25
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.43
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.20
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.15
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.82
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5105.18
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.85
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.53
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.33
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:21.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.87
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :    1.70
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.05

Sample variance                       :    2.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.88e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 5.57e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.60
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.31
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.53
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:04.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.41
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9947.56
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:04:12.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9961

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:51.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.31
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:53.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.23
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4228.43
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11642.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:30.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11899.03
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:30.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.24
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999971237

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.84
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999918686

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    4.91
p-value of test                       :  3.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.86
p-value of test                       :    0.9979

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:11.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:41.12

 All tests were passed




Server wird beendet - Lösche Semaphor 116457480.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:48.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:27.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:53.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4089
p-value of test                       : 1 -  7.6e-5    *****


-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7554
p-value of test                       :  3.1e-3


-----------------------------------------------
CPU time used                    :  00:03:05.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:05.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:57.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:01.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.12
p-value of test                       :    0.9997    *****

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     329
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:12.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.34
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.24
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.36
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.83
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.46
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:43.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1375.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:00.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6931.22
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:41.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:03.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.97
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.58
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4969.01
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:58.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45746
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869746
  j =  1                              :        399908513
  j =  2                              :            45736
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45666
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869666
  j =  1                              :        399908670
  j =  2                              :            45662
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:28.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:19.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  1.0e-2


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:56.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:36.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.02e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.41
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:47.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.52
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.78
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.97
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.29
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17543.11
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.15
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.05
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.12
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.97
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.97
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.99
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.14
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.40
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.86
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.23
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   99.98
p-value of test                       :    0.9911


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.27
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.47
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  103.05
p-value of test                       :    0.9972


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.99
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.63
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.60
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.37
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5250.77
p-value of test                       :  6.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.64
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.21
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.92
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.37
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.95
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  429.39
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.68
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.78
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.66
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -1.31
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.46e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 7.73e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.13
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.51
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.74
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:04.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.49
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:05.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10166.91
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.24
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:43.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4737.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:51.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.49
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3913.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.76
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.74
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.26
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999799700

Normal statistic for number of bits   :   -1.58
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.53
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000077809

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :  -0.073
p-value of test                       :    0.53

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:34.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 16  BirthdaySpacings, t = 7        1 -  7.6e-5
 22  ClosePairs mNP, t = 3           0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 117506056.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:48.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:27.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5490
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:55.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:06.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:56.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:02.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.85
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:12.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    2.97
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     184
p-value of test                       :  4.0e-3

Stat. AD (mNP2)                       :    1.86
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.40
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.84
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.96
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.59
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.99
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  385.95
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:46.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1388.48
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6917.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.02
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9977

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.26
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:02.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.77
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.37
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:32.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5032.10
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:58.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46175
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870175
  j =  1                              :        399907654
  j =  2                              :            46167
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45630
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869630
  j =  1                              :        399908743
  j =  2                              :            45624
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:27.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:16.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:34.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.88e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:21.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:37.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.85
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.00
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.78
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:48.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.19
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.43
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.3e-3

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.28
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17283.35
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.79
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.15
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    9.05
p-value of test                       :    0.9985


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.55
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.49
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.87
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.96
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.55
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.34
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.23
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.21
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.38
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.37
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.99
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.25
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.65
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.75
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.22
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.34
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.12
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.58
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.13
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.39
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:34.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.56
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.00
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5215.51
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.60
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.75
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:33.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.85
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:21.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.31
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -1.22
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:21.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 7.56e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 7.32e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.71
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.06
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.94
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:03.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.66
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:04.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10060.62
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9827.60
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:38.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.47
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.53
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.01
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4250.41
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.39
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.62
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.75
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000061612

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.86
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000085270

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.90

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.24

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:00:57.35

 All tests were passed




Server wird beendet - Lösche Semaphor 118521864.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:47.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:27.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:54.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:06.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:08.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:02.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:04:04.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:12.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:42.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.98
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.96
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.53
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.23
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.10
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  192.52
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.00
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6889.78
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.67
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.95
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:08.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.80
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.58
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5102.46
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:55.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45804
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869804
  j =  1                              :        399908395
  j =  2                              :            45798
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45684
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869684
  j =  1                              :        399908635
  j =  2                              :            45678
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:30.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:03.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:56.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.72e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.62e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    3.24
p-value of test                       :  6.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.32
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.99
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.11
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:45.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.14
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.73
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.32
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17575.57
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.21
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.49
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.21
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.79
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.38
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.47
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.53
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.72
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.48
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.89
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.20
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  173.27
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.41
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.35
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.17
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.23
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.99
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.82
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.66
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.53
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4848.26
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.29
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.92
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.41
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.12
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4879.07
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.05
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  162.88
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.80
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.35
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    1.39
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:20.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.83e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 8.01e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.61
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.11
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:04.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.68
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:05.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9867.34
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10084.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:04:12.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.27
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:52.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.18
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:53.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.05
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4319.47
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.40
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11664.62
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.19
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000042904

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.33
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000047329

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:54.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 55  SampleCorr, k = 1               6.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 119472136.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  7.0e-3


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:48.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:27.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5423
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:55.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:41.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4197
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:58.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:07.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:06.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:56.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:01.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    3.91
p-value of test                       :  9.7e-3

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:15.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    5.96
p-value of test                       :  1.0e-3

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:42.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.79
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.00
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.22
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.99
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.25
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:43.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7080.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.51
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:04.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.60
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.46
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:33.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4907.46
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:58.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45858
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869858
  j =  1                              :        399908289
  j =  2                              :            45848
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45696
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869696
  j =  1                              :        399908608
  j =  2                              :            45696
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.63e-3
p-value of test                       :    0.9914

Anderson-Darling statistic = A2       :    4.95
p-value of test                       :  3.1e-3


-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:20.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :  2.0e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.69
p-value of test                       :  4.2e-3


-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 7.74e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.80
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.12
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.12
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:39.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.72
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.93
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.93
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17087.61
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.60
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.89
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.04
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.27
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.88
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.19
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.71
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.77
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.01
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.89
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.22
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.60
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.00
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.48
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.56
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.59
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.77
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.90
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.98
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.20
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.19
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4898.19
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.63
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.90
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.37
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.26
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.83
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.52
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.63
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.03
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:20.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.63
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:21.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.43e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.85e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.32
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.07
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.68
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:04.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.40
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:06.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.14e-3
p-value of test                       :    0.9968

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9693.34
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10145.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.35
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.054
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:39.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4999.84
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4745.64
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:50.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3976.27
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4025.33
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11797.87
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11609.68
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.12
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000056860

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.78
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999938240

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.75
p-value of test                       :    0.96

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:07.10

 All tests were passed




Server wird beendet - Lösche Semaphor 120487944.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5525
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:55.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:41.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:57.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:06.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:05.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7473
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:56.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7538
p-value of test                       :  5.4e-3


-----------------------------------------------
CPU time used                    :  00:04:01.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.16
p-value of test                       :    0.9977

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    2.27
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:14.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:41.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.32
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.93
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  389.87
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:45.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6968.95
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.80
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:03.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.61
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.26
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4859.22
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:57.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46295
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870295
  j =  1                              :        399907416
  j =  2                              :            46283
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45636
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869636
  j =  1                              :        399908732
  j =  2                              :            45628
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:27.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:45.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:34.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.00e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.94e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.83
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:48.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.02
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.98
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.52
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.64
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.47
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17272.33
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.98
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.70
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.62
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.57
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.54
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.43
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.31
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.27
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.97
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.60
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.95
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.66
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.36
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.29
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.27
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:42.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.20
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.79
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.66
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.44
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.28
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.40
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.20
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.24
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.42
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:34.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.62
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4863.90
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.16
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.98
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:33.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.94
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:15.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.62
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:15.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 6.31e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.53
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.98
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.60
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:56.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.41
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9821.92
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9963

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.44
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.024
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:25.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.25
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:33.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.64
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.18
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11979.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11753.63
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.60
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000124594

Normal statistic for number of bits   :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.78
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000063982

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.92e-3
p-value of test                       :    0.9970

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   0.017
p-value of test                       :    0.49

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.06
p-value of test                       :    0.98

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:57:16.76

 All tests were passed




Server wird beendet - Lösche Semaphor 121503752.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5549
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:41.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:35.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:34.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:54.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:54.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:01.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:01.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:53.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:58.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.15
p-value of test                       :    0.9986


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.93
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:11.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    2.28
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:35.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.35
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.99
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.16
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.86
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1371.84
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7151.16
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:44.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.14
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.06
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:03.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.95
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.96
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:35.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4881.18
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:01.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45737
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869737
  j =  1                              :        399908532
  j =  2                              :            45725
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45539
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869539
  j =  1                              :        399908925
  j =  2                              :            45533
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:30.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:18.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:52.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 9.62e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 3.33e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.45
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:01:35.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.47
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.53
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.13
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.21
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.72
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.48
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:40.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.91
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17416.15
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.89
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.43
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.81
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.28
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.46
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.88
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.54
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.68
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.90
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.60
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.07
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.48
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.36
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.18
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.79
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.06
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.28
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.94
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.26
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.57
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.48
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.36
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.33
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.24
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.64
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  242.03
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.40
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.45
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:17.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 8.64e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.34e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.92
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.94
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.15
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:06.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.80
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:09.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9912.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.25
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.022
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:48.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.16
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.80e-3
p-value of test                       :    0.9971

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5112.14
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.61
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11927.06
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11751.44
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.30
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000001468

Normal statistic for number of bits   :   0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.51
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999977084

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.57e-3
p-value of test                       :    0.9930

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.6e-3

Anderson-Darling statistic = A2       :    4.11
p-value of test                       :  8.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.71
p-value of test                       :  3.4e-3

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:50.19

 All tests were passed




Server wird beendet - Lösche Semaphor 101875721.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5488
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:42.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:37.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:34.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4162
p-value of test                       :    0.9961


-----------------------------------------------
CPU time used                    :  00:01:54.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4225
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:00.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:01.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:54.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:58.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     849
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.82
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:44.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:10.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    3.95
p-value of test                       :  9.3e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    3.72
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:38.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.20
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.41
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.00
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.99
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.92
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.39
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:59.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7004.55
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:53.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:03.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.57
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.15
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:35.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5013.29
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:01.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908340
  j =  2                              :            45824
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45675
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869675
  j =  1                              :        399908651
  j =  2                              :            45673
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:29.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.05e-3
p-value of test                       :    0.9942

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:17.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9970

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:02.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:53.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:32.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.44e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.85
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:48.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.97
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.26
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.92
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.21
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.89
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   11.50
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.20
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17551.21
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.33
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.55
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.58
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.77
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.93
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:39.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.22
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.36
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.81
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.34
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.07
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.60
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.11
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.53
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.12
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.18
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.46
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.65
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.96
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.82
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.84
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.68
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.49
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.61
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  242.16
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.18
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.80
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.40
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.01
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.85
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.65
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:21.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.10
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:18.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.77

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.17e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.82
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.27
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:09.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.25
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:09.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9883.84
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9898.03
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:04:06.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.86
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.45
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.42
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3972.42
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11860.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11818.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:29.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.05
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000144004

Normal statistic for number of bits   :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.52
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000030478

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   0.057
p-value of test                       :    0.48

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:22.52

 All tests were passed




Server wird beendet - Lösche Semaphor 102727689.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:39.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5433
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:46.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:35.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:55.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:00.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:01.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:53.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:57.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     945
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.00
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:10.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9927

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:37.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.72
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.02
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.19
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.83
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.28
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.84
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.87
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7011.31
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.56
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.84
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:03.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.76
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:47.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.07
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:34.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5004.88
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:02.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45733
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869733
  j =  1                              :        399908535
  j =  2                              :            45731
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45843
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869843
  j =  1                              :        399908317
  j =  2                              :            45837
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:29.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:18.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:02.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:32.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 8.12e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.067
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.30
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.93
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.38
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.52
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:47.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.85
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:38.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.36
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.36
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.35
p-value of test                       :  6.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16933.18
p-value of test                       :    0.9964



-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.13
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.06
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.89
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.76
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.40
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.30
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.99
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.34
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.85
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.10
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.63
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.04
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.62
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.39
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.63
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.12
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.77
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.14
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.26
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.00
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.47
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.84
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4876.91
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.48
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.76
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.93
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.83
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.14
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.36
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.28
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.84
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:19.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.28
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:18.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.42e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.31e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 6.21e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.57
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.91
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:08.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.93
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10096.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:54.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4849.92
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:50.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4208.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.35
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.80
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11716.27
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.57
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000083839

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.94
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999910427

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.0e-3

Anderson-Darling statistic = A2       :    5.26
p-value of test                       :  2.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.99
p-value of test                       :  1.4e-3

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:43.80

 All tests were passed




Server wird beendet - Lösche Semaphor 103776265.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:39.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5506
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:50.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:36.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:54.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:54.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:00.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:01.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7477
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:53.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.64
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:03.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:30.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.01
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.58
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.88
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.32
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.62
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  194.45
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.65
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:59.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7071.11
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.84
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:04.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.91
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.44
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5027.79
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:55.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46214
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870214
  j =  1                              :        399907579
  j =  2                              :            46200
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45613
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869613
  j =  1                              :        399908778
  j =  2                              :            45605
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:28.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:17.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:54.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.15e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.04e-5
p-value of test                       :    0.9957

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.91e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.35e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:35.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:34.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.64
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.12
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.22
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:40.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.47
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17431.42
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.30
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.84
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.82
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.24
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.09
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.48
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.04
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.61
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.09
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.50
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.40
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.69
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.80
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.01
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.99
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.41
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.14
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.02
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.27
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.43
p-value of test                       :    0.9907


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.73
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.88
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.28
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.78
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.60
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.75
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.45
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.14
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.31
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.29
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:22.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.53
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -2.03
p-value of test                       :    0.98

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.11e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 9.42e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.29e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.71
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.76
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.53
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:05.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.27
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:06.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9972.37
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9904.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:46.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:48.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.27
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4281.01
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11879.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12193.90
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.76
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000049966

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.42
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999885659

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :  -0.028
p-value of test                       :    0.51

Sample variance                       :    0.23
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:21.25

 All tests were passed




Server wird beendet - Lösche Semaphor 104857609.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5512
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:53.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:38.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:55.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:01.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:01.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:54.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:58.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.97
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:46.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.62
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:10.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.89
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.56
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.18
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.95
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.32
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.15
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:45.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.88
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7046.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.34
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.73
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:04.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.44
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.80
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:32.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5189.70
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:54.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45959
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869959
  j =  1                              :        399908084
  j =  2                              :            45955
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46105
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870105
  j =  1                              :        399907791
  j =  2                              :            46103
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:28.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:18.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:46.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:01.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:55.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:32.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.43e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 2.15e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:33.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:33.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.70
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.09
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.05
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.93
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.64
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:38.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.46
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17211.82
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.27
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.00
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.49
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.27
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.33
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.95
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.39
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.20
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.21
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.51
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.30
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   98.15
p-value of test                       :    0.9940


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.12
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.57
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.75
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.37
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.68
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.82
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.41
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.25
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.50
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.19
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.84
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.56
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.43
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  436.11
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.74
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.10
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:23.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.42
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    1.86
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:22.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9902

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.00e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 9.61e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 3.27e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.04
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.70
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.16
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:06.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.73
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:04.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.14
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.36
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.055
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.018
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:53.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.12
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5048.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:51.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.62
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.10
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11998.02
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:29.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.91
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000006058

Normal statistic for number of bits   :   0.048
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.94
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999838694

Normal statistic for number of bits   :   -1.28
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:13.18

 All tests were passed




Server wird beendet - Lösche Semaphor 105676809.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5463
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:55.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:39.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:55.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:54.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:00.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:01.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:54.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:58.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    2.37
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:09.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     178
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:35.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.81
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.53
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.02
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.81
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.60
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.22
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:02.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6939.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:44.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.93
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.81
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:04.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.70
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.36
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5152.00
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:11.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:58.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45629
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869629
  j =  1                              :        399908744
  j =  2                              :            45625
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908190
  j =  2                              :            45899
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:18.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:45.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:59.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:34.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 9.43e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:34.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.55
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.59
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.01
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.57
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:38.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.68
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.45
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.59
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17880.68
p-value of test                       :  8.3e-3



-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.03
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.64
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.39
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.58
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.60
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.11
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.10
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.46
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.59
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.38
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.98
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.05
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.20
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.93
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.97
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.10
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.01
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  469.67
p-value of test                       :  1.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.77
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.25
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.20
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.92
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.22
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.18
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5132.55
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.88
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.26
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.67
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:22.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.91
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   0.061
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:21.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.98

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 3.47e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.36
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.38
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:04.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.09
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:05.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.00
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9840.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.091
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:43.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.57
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4738.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:51.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.06
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.60
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.52
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.09
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000074923

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.25
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999939671

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :  -0.090
p-value of test                       :    0.54

Sample variance                       :    2.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         : 9.30e-3
p-value of test                       :    0.50

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:47.62

 All tests were passed




Server wird beendet - Lösche Semaphor 106659849.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5432
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:58.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:41.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:02.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7511
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:03.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:57.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:10.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:39.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.84
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.69
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.20
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.84
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.81
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.98
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.50
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1376.05
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7169.99
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.35
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:08.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.85
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.49
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5014.76
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:54.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45747
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869747
  j =  1                              :        399908511
  j =  2                              :            45737
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45718
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869718
  j =  1                              :        399908570
  j =  2                              :            45706
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:29.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  9.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:18.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:03.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.50e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.08e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.63
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.61
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.85
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.80
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.73
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.73
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17244.38
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.97
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.17
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.54
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.47
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.49
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.13
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.18
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.38
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.88
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.76
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.84
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.74
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.79
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.27
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.45
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.11
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.66
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.53
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.44
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.91
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.70
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  440.18
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.42
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.29
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.28
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.82
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.56
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.20
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:34.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.50
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.19
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -1.21
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:21.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9946

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    2.55
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.33e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 6.16e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.95e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.49
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.33
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.25
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:04.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10029.94
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:04:19.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5002.64
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:52.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.7e-3

Anderson-Darling statistic = A2       :    3.82
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5114.83
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:53.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.97
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.71
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11657.29
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11868.21
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.49
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000003268

Normal statistic for number of bits   :   0.026
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.44
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999957200

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :  -0.022
p-value of test                       :    0.51

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:16.02

 All tests were passed




Server wird beendet - Lösche Semaphor 107708425.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:56.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:02.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:03.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:55.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:58.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:44.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:05.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:33.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.56
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.69
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.74
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.79
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7003.04
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.12
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.64
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:04.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.07
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.31
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5155.19
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:53.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45810
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869810
  j =  1                              :        399908384
  j =  2                              :            45802
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45510
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869510
  j =  1                              :        399908985
  j =  2                              :            45500
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:26.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 5.52e-3
p-value of test                       :    0.9935

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:17.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:56.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:34.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.83e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 2.97e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:36.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.01
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.33
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.32
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.45
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.85
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:37.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.66
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.02
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.74
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17455.99
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   63.62
p-value of test                       :  3.0e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.76
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.51
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.23
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.52
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.83
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.42
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.55
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.00
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.69
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.35
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.86
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.03
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.20
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.21
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.50
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.20
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.38
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.86
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.66
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.30
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.95
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.65
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.46
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.72
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.84
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.75
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  436.88
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.93
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.30
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :    2.54
p-value of test                       :  5.6e-3



-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.07
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -1.46
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.30e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.48e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.07
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.41
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.70
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:04.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.4e-3

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.15
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:05.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 7.44e-3
p-value of test                       :    0.9920

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9817.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:44.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5030.21
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  2.8e-3

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5093.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.50
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.76
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12025.22
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11825.81
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.95
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000128461

Normal statistic for number of bits   :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.22
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999939266

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:04.55

 All tests were passed




Server wird beendet - Lösche Semaphor 108822537.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:57.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:03.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:03.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:55.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:00.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.82
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:16.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:46.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.35
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.39
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.58
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.49
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.56
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.01
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.59
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:02.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7021.35
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:44.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.29
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.55
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:04.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.94
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.18
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5197.84
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:54.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46147
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870147
  j =  1                              :        399907709
  j =  2                              :            46141
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45549
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869549
  j =  1                              :        399908908
  j =  2                              :            45537
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:27.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:17.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:45.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:58.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:33.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.22e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.98
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.52
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.86
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.83
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.60
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.46
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.64
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.18
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.70
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.80
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17277.15
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.34
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.17
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.73
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.27
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.78
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.68
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.29
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.94
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.55
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.06
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.94
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.85
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.52
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.47
p-value of test                       :    0.9905


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.46
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.75
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.61
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.75
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.70
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  458.89
p-value of test                       :  5.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.22
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.33
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.85
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.58
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.92
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.21
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5113.22
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.16
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  251.94
p-value of test                       :  7.5e-3


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.60
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -1.28
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.37
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:23.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.13

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.46e-3
p-value of test                       :    0.9909

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.98
p-value of test                       :    0.02

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.77e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.78e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.92
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.39
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:05.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:06.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.02
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:41.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5000.50
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5036.65
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:50.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11678.65
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11924.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.66
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999942170

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.00
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999982340

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:24.20

 All tests were passed




Server wird beendet - Lösche Semaphor 109772809.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5461
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:57.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:41.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:05.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:05.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:55.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:01.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:45.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:12.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:39.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.54
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    5.00
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.11
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.26
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.58
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.74
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.64
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:45.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1390.64
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7312.37
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:43.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.69
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.21
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:05.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.74
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  155.86
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5015.69
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:00.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45572
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869572
  j =  1                              :        399908858
  j =  2                              :            45568
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45740
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869740
  j =  1                              :        399908524
  j =  2                              :            45732
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:21.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:27.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:20.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :  1.4e-3

Anderson-Darling statistic = A2       :    4.96
p-value of test                       :  3.1e-3


-----------------------------------------------
CPU time used                    :  00:01:59.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :  1.1e-3

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:34.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 3.86e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.65
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.55
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.40
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:48.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.32
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.53
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.89
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   99.86
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17483.97
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.92
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.84
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.34
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.25
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.91
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.68
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.05
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.98
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.71
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.98
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.55
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.10
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.03
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.54
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.29
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.25
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.86
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.43
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.58
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.46
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.16
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.36
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.80
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.47
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.07
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.14
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.27
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.34
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.33
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.84
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :    1.97
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:22.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.20
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -1.88
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:22.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.73
p-value of test                       :    0.96

Sample variance                       :    0.22
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.35e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.32
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.95
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.50
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:04.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.18
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:06.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9952.43
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10305.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:41.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5035.63
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.65
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:50.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.45
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.52
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11851.37
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.19
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999985448

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.03
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000101935

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:11.38

 All tests were passed




Server wird beendet - Lösche Semaphor 110755849.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:59.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:43.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4457
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:54.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:00.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    3.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.13
p-value of test                       :    0.9996    *****

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:13.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    3.15
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     116
p-value of test                       :    0.9977

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:42.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.91
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.91
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.00
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1282.22
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7252.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.34
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:03.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.72
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.27
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:32.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5024.83
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:01.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45999
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869999
  j =  1                              :        399908007
  j =  2                              :            45989
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46091
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870091
  j =  1                              :        399907819
  j =  2                              :            46089
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:26.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:19.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:59.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:34.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.82e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.081
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.030
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:35.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:35.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   39.98
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.21
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:47.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.31
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   61.97
p-value of test                       :  3.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:36.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.03
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.83
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17440.47
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.68
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   44.48
p-value of test                       :  9.6e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.03
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.31
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.79
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.41
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.94
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.09
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.74
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.21
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.23
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.16
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.12
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.21
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.09
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.85
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  595.00
p-value of test                       :  2.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.34
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.56
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.41
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.74
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.39
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.31
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  146.50
p-value of test                       :    0.9983


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.73
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.17
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4876.99
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.93
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.60
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.36
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:22.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.06
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:23.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.67e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.23e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 5.11e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.76
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.61
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:04.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.01
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10150.61
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10161.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:40.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4996.33
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:47.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4735.92
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4229.97
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.19
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12064.88
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.84
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000019639

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.62
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000013750

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :  -0.094
p-value of test                       :    0.54

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.088
p-value of test                       :    0.47

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:39.18
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP2, t = 9          0.9996 
 65  SumCollector                    3.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 111771657.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:57.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7164
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:42.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:57.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:05.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:55.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7493
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:59.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     947
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    2.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:51.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:14.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:40.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.94
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.09
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.94
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.14
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.48
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.78
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.39
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:01.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7037.64
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:44.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.63
p-value of test                       :  9.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.75
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:04.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.30
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.71
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4787.91
p-value of test                       :    0.9944


-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:57.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45730
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869730
  j =  1                              :        399908545
  j =  2                              :            45720
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45606
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869606
  j =  1                              :        399908790
  j =  2                              :            45602
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:25.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:18.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:47.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:54.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:32.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.28e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 6.24e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    3.67
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:37.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   73.59
p-value of test                       :  9.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.14
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.039
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.95
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17301.08
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   14.56
p-value of test                       :    0.9991    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.88
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.04
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.17
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.21
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.10
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.28
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.93
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.68
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.87
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.63
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.94
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.47
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.81
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.15
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   99.36
p-value of test                       :    0.9922


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.32
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.02
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.51
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.61
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.49
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.58
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.37
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.29
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.27
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.61
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.30
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.62
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -1.69
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:22.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    2.77
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:01:10.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.52e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.36
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.02
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.28
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:03.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:04.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9908.61
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.27
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:49.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.62
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:48.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4728.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3984.36
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.48
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11732.95
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.70
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.12
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999918977

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.41
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999893975

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:02.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 66  MatrixRank, L=30, r=0           9.5e-4
 74  RandomWalk1 M (L=50, r=0)       0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 112787465.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:58.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:42.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:06.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7478
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:55.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7154
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:00.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     329
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:14.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    2.06
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:42.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.99
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.04
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.37
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.72
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.07
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.60
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.74
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.58
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.18
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:03.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6948.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:45.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.93
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.30e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   38.58
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:03.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.29
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.08
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5134.12
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:11.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:00.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45897
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869897
  j =  1                              :        399908206
  j =  2                              :            45897
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45680
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869680
  j =  1                              :        399908642
  j =  2                              :            45676
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:26.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:19.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:03.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:54.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:34.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.25e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.070
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.042
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:34.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.53
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.72
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.61
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.61
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.35
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.40
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:37.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9907

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.97
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.77
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17365.78
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.86
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.33
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.44
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.09
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.26
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.86
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.74
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.01
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.11
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.74
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.35
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.31
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.88
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.41
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.68
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.59
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.14
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.96
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.13
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.13
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.20
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.92
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.51
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.28
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.25
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.47
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4856.25
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.72
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.33
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.99
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:23.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.72
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:23.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.24e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 5.53e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 9.15e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.27
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.86
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:03.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.56
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:04.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10102.80
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.76
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:39.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5020.39
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4768.76
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:49.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4220.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.26
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12023.74
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11899.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.66
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999929702

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.00
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999892157

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.4e-3

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.15
p-value of test                       :    0.02

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:55.02

 All tests were passed




Server wird beendet - Lösche Semaphor 113803273.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1482
p-value of test                       :  8.6e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334602
  j =  1                              :        599997036
  j =  2                              :             1482
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:58.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:42.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:06.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:07.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:57.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:01.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.82
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.71
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:14.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:42.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.80
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.27
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.80
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.75
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.47
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.18
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.91
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.49
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1363.87
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:01.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6934.18
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.43
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:02.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.72
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.85
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:30.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5002.40
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:00.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45950
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869950
  j =  1                              :        399908102
  j =  2                              :            45946
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46082
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870082
  j =  1                              :        399907838
  j =  2                              :            46078
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:27.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-3
p-value of test                       :    0.9981

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:18.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.79
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:54.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.28e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:32.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:48.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.13
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.00
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.58
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.98
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17529.91
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.00
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.12
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.63
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.98
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.94
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.29
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.62
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.67
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.97
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.19
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.32
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.30
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.41
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.28
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.75
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.72
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.41
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  173.76
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.07
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.64
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4824.78
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.14
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.30
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.99
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.26
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.29
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.70
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.83
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.87
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -2.66
p-value of test                       :    0.9961



-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.14
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:22.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.68e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.88
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.98
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.43
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:04.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.64
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:06.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9846.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10084.39
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:36.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.04
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.20
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.53
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.52
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11607.92
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11700.74
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.87
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999910661

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.49
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000123199

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:34.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  3  CollisionOver, t = 2            8.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 114819081.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:58.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:41.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:06.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:05.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:57.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:01.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     939
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.81
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    2.45
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:14.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.18
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.86
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.18
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.95
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.83
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.54
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1497.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6998.20
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:45.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.00
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:01.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.49
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.13
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5094.98
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:58.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45701
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869701
  j =  1                              :        399908601
  j =  2                              :            45695
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45906
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869906
  j =  1                              :        399908191
  j =  2                              :            45900
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:26.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:18.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:54.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 8.22e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 9.12e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:47.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.01
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.28
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:47.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.24
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.39
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.72
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    4.67
p-value of test                       :  4.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.58
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17527.00
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.10
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.17
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.85
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.34
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.86
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.15
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   44.66
p-value of test                       :  9.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.60
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.05
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.41
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.32
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.74
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.87
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.76
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.65
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.91
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.61
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.11
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.83
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.05
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.34
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.19
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.13
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.02
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.99
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.64
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  436.20
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.34
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.94
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:22.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.02
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:22.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.21e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.00e-2
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.97
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.07
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.20
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:03.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.68
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:04.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.99
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9981.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.030
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:40.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:47.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4754.73
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:49.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.96
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11853.13
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11690.38
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.63
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000031276

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.74
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999890507

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:07.70

 All tests were passed




Server wird beendet - Lösche Semaphor 115802121.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:59.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:45.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:02.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:13.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:09.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:14.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:51.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.33
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:15.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    2.77
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.18
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.12
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.04
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.62
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.63
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.77
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.20
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:29.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  497.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:57.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1506.77
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:07.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7039.80
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.48
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.75
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:16.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.73
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.03
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5231.58
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:02.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45634
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869634
  j =  1                              :        399908735
  j =  2                              :            45628
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45615
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869615
  j =  1                              :        399908776
  j =  2                              :            45603
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:31.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:21.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-3
p-value of test                       :    0.9982

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  6.7e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:54.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:10.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:56.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:38.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 2.40e-6
p-value of test                       :    0.9998    *****

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.31e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:25.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : 1.49e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:52.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.64
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.17
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.42
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:52.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.13
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.46
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.06
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.99
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17289.47
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.92
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.85
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.85
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.98
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.87
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.19
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.10
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.28
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.79
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.63
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.53
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.78
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.41
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.08
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.03
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.18
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.95
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.84
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.43
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.74
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.02
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.65
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.70
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:34.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.49
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.28
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.47
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.82
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:34.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.34
p-value of test                       :    0.9927


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:22.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.15
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:20.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.89e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.02e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.57
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.32
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.43
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.27
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:04.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9751.38
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.64
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:13.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:04:37.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.55
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:52.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.72
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:58.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3889.17
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12060.62
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:34.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11734.46
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.76
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999970733

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.35
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000137908

Normal statistic for number of bits   :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   0.080
p-value of test                       :    0.47

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:32.46

 All tests were passed




Server wird beendet - Lösche Semaphor 116817929.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1255
p-value of test                       :    0.9986

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334375
  j =  1                              :        599997490
  j =  2                              :             1255
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5442
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:58.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7483
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:07.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:05.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:56.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:01.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    7.81
p-value of test                       :  1.5e-4    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     952
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:51.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:19.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:48.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.50
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.58
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.69
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.19
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.23
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.76
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.95
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.88
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:44.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.21
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:02.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7030.66
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:42.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:04.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.24
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:31.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5100.78
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:07.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46113
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870113
  j =  1                              :        399907775
  j =  2                              :            46111
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45732
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869732
  j =  1                              :        399908539
  j =  2                              :            45726
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:26.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:17.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 8.63e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:01.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.77e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.19e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:35.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.13
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.30
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.41
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.93
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.10
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.65
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.29
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.03
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17567.12
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.45
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.55
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.55
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.77
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   12.49
p-value of test                       : 1 -  9.3e-5    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.13
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.91
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.78
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.11
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.17
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.33
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.12
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.29
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.92
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.01
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.36
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.43
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.87
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.72
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.79
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.53
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5085.43
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.38
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.92
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.06
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.30
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.99
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.22
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.29
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.77
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:21.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.94
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 8.82e-4
p-value of test                       :    0.9991    *****

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.15
p-value of test                       :    0.98

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-4
p-value of test                       :    0.9918

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.74e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.84
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.89
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:05.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.12
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9718.39
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10024.56
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:55.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:41.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4717.13
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.32
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.81
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11649.79
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11922.57
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.35
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999804332

Normal statistic for number of bits   :   -1.55
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.71
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000107953

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:41.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs NP, t = 3            1.5e-4
 75  RandomWalk1 H (L=50, r=25)     1 -  9.3e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 117997577.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5403
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:57.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:58.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:06.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:06.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:57.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:02.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.44
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    3.85
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:17.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:48.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.28
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.16
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.39
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.28
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.11
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.78
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.06
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.64
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:44.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1534.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:02.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7045.10
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:05.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.28
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.25
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5034.48
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:01.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45784
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869784
  j =  1                              :        399908434
  j =  2                              :            45780
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45943
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869943
  j =  1                              :        399908117
  j =  2                              :            45937
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:25.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:17.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:59.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:33.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.01e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.83e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:34.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:32.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.84
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.37
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.22
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.00
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:48.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.17
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.82
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.11
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:38.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.04
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.22
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17583.16
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:52.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.79
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.27
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.93
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.93
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.56
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.21
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.34
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.77
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.89
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.61
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.45
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.27
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.06
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.60
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.79
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.91
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.49
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.78
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.22
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.50
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.68
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.47
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5296.37
p-value of test                       :  1.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.47
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.20
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:34.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.83
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.02
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.67
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.00
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.89
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:22.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.63
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -1.15
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    3.33
p-value of test                       :  4.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 3.51e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.18e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.01
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.23
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.97
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:04.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.40
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:06.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.29
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9967.73
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:41.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.08
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.25
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11464.73
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.87
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.95
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999984719

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.23
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000060901

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:31.53

 All tests were passed




Server wird beendet - Lösche Semaphor 119013385.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:56.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:41.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:04.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:55.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:00.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    2.33
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.58
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:17.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    3.61
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:45.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.99
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.61
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.66
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.76
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.78
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.30
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.50
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.13
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:02.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7064.46
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:43.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.10
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.96
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:03.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.97
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.41
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5115.39
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:11.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:01.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45584
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869584
  j =  1                              :        399908835
  j =  2                              :            45578
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45695
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869695
  j =  1                              :        399908611
  j =  2                              :            45693
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:24.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:17.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:45.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:54.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.65e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.87e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.74
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.67
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:37.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.46
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.18
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.61
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17644.23
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.81
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.25
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.73
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.77
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.74
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.83
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.83
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.69
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.74
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.25
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.51
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.36
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.21
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.97
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.86
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.26
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.63
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.63
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.61
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  454.67
p-value of test                       :  7.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.84
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5119.87
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.11
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.04
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.97
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.37
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.81
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.43
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  147.11
p-value of test                       :    0.9981


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.23
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:21.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.98
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.56e-4
p-value of test                       :    0.9993    *****

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.4e-3

Anderson-Darling statistic = A2       :    4.86
p-value of test                       :  3.5e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.23
p-value of test                       :  6.2e-4    *****

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 7.24e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.69
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.93
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.85
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:04.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.41
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9850.70
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.17
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.051
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:42.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5082.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.62
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:50.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.98
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11873.55
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.36
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999888731

Normal statistic for number of bits   :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.84
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999995231

Normal statistic for number of bits   :  -0.038
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9980

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.26
p-value of test                       :    0.01

Sample variance                       :    3.00
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:35.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 83  LempelZiv, r = 15               6.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 120029193.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5501
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:57.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:43.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:02.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:09.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:09.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:03.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:07.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    2.38
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.56
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     329
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:18.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.24
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:47.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.85
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.29
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.27
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.02
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.91
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.37
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7099.16
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.70
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:08.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.30
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.61
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4850.33
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:13.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45953
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869953
  j =  1                              :        399908094
  j =  2                              :            45953
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45830
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869830
  j =  1                              :        399908341
  j =  2                              :            45828
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :  3.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:27.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:17.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 8.46e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.077
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.15
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.23
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.75
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.23
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.16
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.32
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.81
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.26
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17425.55
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.65
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.12
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.25
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.71
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.30
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.46
p-value of test                       :    0.9967


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.54
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.27
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.76
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.99
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.35
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.12
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.98
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.43
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.69
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.18
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.07
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.72
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.69
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.33
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.50
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.57
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.39
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.95
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.91
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.74
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.73
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  264.20
p-value of test                       :  1.6e-3


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.00
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   0.097
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:21.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.57
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    0.57
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.02
p-value of test                       :    0.98

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.80
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.66
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.50
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:05.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9815.09
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10049.61
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:04:17.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5039.13
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:51.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.01
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:53.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4221.57
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4235.38
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11900.88
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11919.85
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:30.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.12
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999952283

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.71
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999948881

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:05.42

 All tests were passed




Server wird beendet - Lösche Semaphor 121045001.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:42.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:34.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:03.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:03.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:59.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7158
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:03.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.09
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:08.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:40.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.02
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.06
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.81
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.41
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.98
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.31
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:50.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.72
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6847.05
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.20
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:17.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.71
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.79
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5018.16
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:24.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45608
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869608
  j =  1                              :        399908786
  j =  2                              :            45604
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46096
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870096
  j =  1                              :        399907812
  j =  2                              :            46088
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.19e-3
p-value of test                       :    0.9988

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9980


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:30.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:17.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    4.69
p-value of test                       :  4.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9929


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:54.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.85
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.10
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.70
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.41
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.10
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.89
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:51.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.79
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.02
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.45
p-value of test                       :  5.4e-3

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17286.23
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.86
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.82
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.87
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.27
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.08
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.96
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.94
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.32
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.71
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.75
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.41
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.55
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.27
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   46.38
p-value of test                       :    0.9951


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.50
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.43
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.77
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.21
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.86
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.54
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.98
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.39
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.65
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.66
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.06
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5080.27
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.30
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.63
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.24
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:27.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.00
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:28.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.86
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.71
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.58
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:06.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10179.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : -7.43e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:04:28.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.25
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.21
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:59.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11555.62
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:34.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11917.68
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:36.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.73
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000007432

Normal statistic for number of bits   :   0.059
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.73
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999957164

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:18:24.82

 All tests were passed




Server wird beendet - Lösche Semaphor 101908490.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:47.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1261
p-value of test                       :    0.9975

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334381
  j =  1                              :        599997478
  j =  2                              :             1261
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:48.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:37.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:02.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:03.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:52.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:01.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    2.02
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:15.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.05
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     124
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.14
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:02:45.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.07
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.10
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.22
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.06
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.75
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  182.77
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  392.12
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:45.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1474.55
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:01.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7026.78
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:44.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.27
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.3e-3

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.18
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:05.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.33
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.76
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:34.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5068.32
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  3.4e-3


-----------------------------------------------
CPU time used                    :  00:03:10.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45917
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869917
  j =  1                              :        399908171
  j =  2                              :            45907
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45572
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869572
  j =  1                              :        399908863
  j =  2                              :            45558
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:24.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:15.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:43.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:54.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:32.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.15e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 3.38e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:34.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.91
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.32
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.63
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.14
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.11
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.78
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17474.93
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.92
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.57
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.61
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.63
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.51
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.58
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.39
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.97
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.30
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.81
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.93
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.40
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  173.40
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.39
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.66
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.48
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.67
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.84
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.52
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.94
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.93
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.07
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.93
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.91
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.75
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.53
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.63
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.84
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.31
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.23
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :   -1.15
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:23.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.33e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.51
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.40
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.07
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:07.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.63
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:07.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:43.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5042.70
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:51.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.11
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.10
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11653.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.48
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:29.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.15
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999929753

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.79
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999865439

Normal statistic for number of bits   :   -1.06
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.33
p-value of test                       :    0.9902

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:06.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP2S, t = 16        0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 103448586.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1468
p-value of test                       :  2.8e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334588
  j =  1                              :        599997064
  j =  2                              :             1468
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5535
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:48.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:37.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:38.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7509
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:05.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:05.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:01.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:12.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:17.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:44.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   20.64
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.13
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.97
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.80
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  262.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.29
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:56.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1371.08
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:04.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7201.07
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.67
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:18.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.84
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:46.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.73
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4941.24
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:10.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45609
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869609
  j =  1                              :        399908784
  j =  2                              :            45605
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45851
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869851
  j =  1                              :        399908299
  j =  2                              :            45849
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:31.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:20.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  9.7e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:03.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 6.91e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.20e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.31e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:50.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.78
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.41
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.23
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.95
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.46
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.39
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.17
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.44
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.08
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.48
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.38
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17282.48
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.99
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.22
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.85
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.15
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.36
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.41
p-value of test                       :    0.9905


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.81
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.84
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.81
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.07
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.09
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.08
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.47
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.57
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.27
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.85
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.80
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.16
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.17
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.78
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.41
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.12
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.89
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.42
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.38
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4896.41
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.84
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.22
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.02
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:23.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.49
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:25.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.2e-3

Anderson-Darling statistic = A2       :    4.70
p-value of test                       :  4.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.84
p-value of test                       :  2.3e-3

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.99e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 2.17e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.94e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.05
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.64
p-value of test                       :  8.2e-3

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.72
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:06.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.05
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:06.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10260.22
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.55
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:04:32.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.96
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.53
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11553.10
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:32.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11862.42
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:33.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.72
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999966470

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.98
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000010882

Normal statistic for number of bits   :   0.086
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:02.25

 All tests were passed




Server wird beendet - Lösche Semaphor 104333322.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1471
p-value of test                       :  2.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334591
  j =  1                              :        599997058
  j =  2                              :             1471
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:48.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4448
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:39.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:36.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:05.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:04.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7531
p-value of test                       :  6.8e-3


-----------------------------------------------
CPU time used                    :  00:03:55.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:01.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    2.32
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:11.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:40.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.21
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.54
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.79
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.71
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.01
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  494.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1567.28
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7223.93
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.70
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.20
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:03.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.75
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:55.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.34
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4887.57
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:33.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46106
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870106
  j =  1                              :        399907792
  j =  2                              :            46098
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46228
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870228
  j =  1                              :        399907548
  j =  2                              :            46220
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:25.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:16.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:44.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:53.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:32.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.30e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.075
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:38.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.41
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:48.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.99
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.06
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.42
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.99
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.58
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:40.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.17
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.79
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.98
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.42
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.00
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17493.92
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.24
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.55
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.03
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.63
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.26
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.05
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.44
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.64
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.18
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.14
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.51
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.83
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.41
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.07
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.64
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.66
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.92
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.73
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.31
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.59
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.72
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.57
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  317.82
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.29
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.77
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.44
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.53
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.69
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.23
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.56
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   0.092
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.19
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:24.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    2.47
p-value of test                       :  8.1e-3

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.18e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 8.81e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.75
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.08
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.83
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:07.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.76
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:06.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9742.60
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9853.42
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9926

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.44
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:47.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:50.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.39
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.25
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.02
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11850.40
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.67
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999934844

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.22
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999831638

Normal statistic for number of bits   :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    2.48
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   0.093
p-value of test                       :    0.46

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:00.96

 All tests were passed




Server wird beendet - Lösche Semaphor 105545738.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5496
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:50.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:38.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:36.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4209
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:04.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:57.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:03.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:49.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.24
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:14.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:44.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.38
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.17
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.75
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.81
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6922.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.73
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.67
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:03.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.58
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.59
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:33.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5141.57
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:58.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45648
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869648
  j =  1                              :        399908708
  j =  2                              :            45640
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45650
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869650
  j =  1                              :        399908704
  j =  2                              :            45642
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  6.6e-3

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  8.2e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:27.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:01.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:54.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:32.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.59e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 5.71e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:32.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:35.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:48.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.92
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.88
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.14
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.35
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.11
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.88
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.24
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.01
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17676.76
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.63
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.46
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.94
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.65
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.22
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.98
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   64.54
p-value of test                       :  1.7e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.38
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.99
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.13
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.48
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.25
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.01
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.49
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.68
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.89
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.91
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.14
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.05
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.71
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.91
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.01
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.84
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.83
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.44
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  462.94
p-value of test                       :  3.5e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.87
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  319.77
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.95
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.33
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:21.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.13
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:23.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.89e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 4.33e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.96
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.40
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.91
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:08.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.64
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:07.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.09
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9892.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:41.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.97
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.24
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:50.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.82
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4010.22
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11993.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12044.23
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.40
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000065599

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.39
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999751835

Normal statistic for number of bits   :   -1.96
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:39.70

 All tests were passed




Server wird beendet - Lösche Semaphor 106430474.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5419
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:50.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:36.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:55.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4474
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:04.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:05.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:54.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:01.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:12.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:40.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.68
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.07
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.69
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.22
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1486.96
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:00.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7168.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:40.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.22
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.92
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:10.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.77
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.69
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5096.68
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:53.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45844
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869844
  j =  1                              :        399908316
  j =  2                              :            45836
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45938
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869938
  j =  1                              :        399908130
  j =  2                              :            45926
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:27.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:17.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:55.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 3.86e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.67e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:26.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.36
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.70
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.72
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.05
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.09
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.73
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.50
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17493.98
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.42
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.35
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.37
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.39
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.59
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.75
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.72
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.93
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.38
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.70
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.99
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.16
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.82
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.32
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.09
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.74
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.21
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.36
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.63
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.52
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.63
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.74
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.87
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.57
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.38
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.16
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4823.38
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.29
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.15
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.74
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:25.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.73
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:24.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.14e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.58
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.62
p-value of test                       :  8.2e-3

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.67
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:05.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.67
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10129.63
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.05
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:42.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.66
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11918.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12390.86
p-value of test                       :  1.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:29.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.48
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999965930

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.21
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000091066

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.6e-3

Anderson-Darling statistic = A2       :    3.84
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.39
p-value of test                       :  8.4e-3

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :  -0.037
p-value of test                       :    0.51

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:01.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 100  HammingIndep, L=1200, r=25      1.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 107347978.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5358
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:51.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4200
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:37.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4215
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:03.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:04.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:55.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:00.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.03
p-value of test                       :  8.6e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.98
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:13.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:44.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.70
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.10
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.40
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.16
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.17
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:43.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.32
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:01.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6930.50
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.04
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:03.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.32
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.15
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:34.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4928.41
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:59.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45920
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869920
  j =  1                              :        399908162
  j =  2                              :            45916
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46015
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870015
  j =  1                              :        399907976
  j =  2                              :            46003
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:27.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:18.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.51e-3
p-value of test                       :    0.9900

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.04e-3
p-value of test                       :    0.9956

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :  3.0e-4    *****

Anderson-Darling statistic = A2       :    7.08
p-value of test                       :  3.2e-4    *****


-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.18e-3
p-value of test                       :    0.9905

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:54.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 7.92e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.28e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.59
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:35.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.61
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   38.96
p-value of test                       :    0.9976

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.53
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   11.61
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:01:39.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.01
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.92
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17277.39
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.77
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.84
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.48
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.77
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.29
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.56
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.18
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.10
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.19
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.68
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.97
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.91
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.65
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.28
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.58
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.47
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.24
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.58
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.27
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.85
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  440.85
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.80
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  319.77
p-value of test                       :    0.9926


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.89
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.39
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.76
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.53
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.69
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:25.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.22
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:24.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 3.00e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 5.80e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.56
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.06
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.44
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:05.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.55
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:06.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9793.99
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:42.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4958.06
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:50.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4274.34
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4265.59
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.52
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.10
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.10
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000012535

Normal statistic for number of bits   :   0.099
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.52
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999980591

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   0.043
p-value of test                       :    0.48

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:47.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 48  MaxOft AD, t = 24               3.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 108331018.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:51.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:38.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4196
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7164
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:03.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:04.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:53.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:59.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:46.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    2.26
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:12.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    2.09
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:41.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   21.99
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.62
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.17
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.85
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.56
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.88
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.30
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.20
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:01.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7040.03
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.56
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.09
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:02.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.66
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.50
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4989.40
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:54.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46024
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870024
  j =  1                              :        399907956
  j =  2                              :            46016
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45959
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869959
  j =  1                              :        399908083
  j =  2                              :            45957
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.60e-3
p-value of test                       :    0.9960

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:17.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:00.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:53.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:33.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:35.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:35.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.18
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.22
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.45
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:38.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.16
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.28
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17245.41
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.92
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.12
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.39
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.32
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.02
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.92
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.76
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.22
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.91
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.26
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.58
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.61
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.25
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.21
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.31
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.43
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.24
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.71
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.80
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.46
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.02
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.12
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.97
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.79
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.48
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.95
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.21
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -1.49e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:24.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.29
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:25.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 7.29e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 9.30e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.73
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.13
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.87
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:05.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:05.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.97
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10112.17
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:44.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.08
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4721.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.98
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.51
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11633.88
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11839.78
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.55
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000023689

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.09
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999907532

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:07.45

 All tests were passed




Server wird beendet - Lösche Semaphor 109215754.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:53.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4447
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:03.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:03.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:55.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:00.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:17.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:45.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.05
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.09
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.95
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.12
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.61
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.30
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.30
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.13
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1514.32
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7244.06
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.06
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.87
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:03.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.81
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.93
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:34.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4951.74
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:55.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45844
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869844
  j =  1                              :        399908317
  j =  2                              :            45834
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45786
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869786
  j =  1                              :        399908432
  j =  2                              :            45778
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:28.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :  3.9e-3

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:18.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9943


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:45.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 3.63e-3
p-value of test                       :    0.9958

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:53.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:32.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 3.51e-4
p-value of test                       :  7.2e-3

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:38.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.34
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.30
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.75
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.78
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.53
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.65
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.01
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.16
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.67e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.82
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17539.55
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.55
p-value of test                       :    0.9959


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.99
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.70
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.72
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.15
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.19
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.76
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.53
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.54
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.10
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.70
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.31
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.20
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.23
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.41
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.25
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.34
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.77
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.75
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.14
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.03
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5106.90
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.25
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.68
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.49
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  482.71
p-value of test                       :  4.5e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.39
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.35
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.11
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.84
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :   -1.44
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.22
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -1.96
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:24.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.17
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 7.67e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.76
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.85
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.93e-3
p-value of test                       :    0.9948

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  160.65
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:05.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.83
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9843.40
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9798.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:45.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4753.88
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4801.67
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4013.66
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.47
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11632.56
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11800.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:29.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.16
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999871274

Normal statistic for number of bits   :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.53
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999959066

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    0.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9905

Tests on the sum of all N observations
Standardized normal statistic         :  -0.072
p-value of test                       :    0.53

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.73
p-value of test                       :    0.96

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:36.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 M (L=10000, r=15)   4.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 110166026.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5376
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:53.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7170
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:03.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:04.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:54.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7501
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:59.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.50
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.93
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:17.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:46.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.57
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.10
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.60
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.21
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.84
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.39
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.62
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.44
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:58.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7206.83
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.90
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.65e-3
p-value of test                       :    0.9962

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.70
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:03.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.65
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.40
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:35.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4970.75
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:17.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46045
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870045
  j =  1                              :        399907913
  j =  2                              :            46039
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45969
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869969
  j =  1                              :        399908065
  j =  2                              :            45963
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:28.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  7.4e-3

Kolmogorov-Smirnov- statistic = D-    : 2.31e-3
p-value of test                       :    0.9975

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9951


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:53.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.7e-3

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.55e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.64e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.31
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.53
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.42
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.60
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.59
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.85
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.08
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:40.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.18
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.35
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.59
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17338.18
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.99
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.93
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.94
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.14
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.75
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.86
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.29
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.03
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.36
p-value of test                       :    0.9943


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.41
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.27
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.04
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.73
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.50
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.14
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.36
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.97
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.67
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.88
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.72
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.63
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.07
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.28
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.59
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.98
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4872.68
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.51
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.10
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.46
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :   0.092
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.96
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -1.88
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:23.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.24
p-value of test                       :    0.99

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.45e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 9.05e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 3.27e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.38
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.81
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.89
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:07.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9902.31
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.89
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.90
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:43.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4933.23
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.98
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:51.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3993.79
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.70
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11980.03
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11993.14
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.09
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000059014

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.64
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000091126

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.74
p-value of test                       :    0.04

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:37.52

 All tests were passed




Server wird beendet - Lösche Semaphor 111149066.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5527
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:55.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:03.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:03.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:54.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:59.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     539
p-value of test                       :    0.9939

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9911


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:16.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:49.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.37
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.53
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.47
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.39
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.66
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.29
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  286.46
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.85
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:02.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6912.21
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:42.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.76
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:03.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.72
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.42
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5216.34
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:13.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45710
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869710
  j =  1                              :        399908584
  j =  2                              :            45702
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45813
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869813
  j =  1                              :        399908381
  j =  2                              :            45799
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:28.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:18.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 6.66e-3
p-value of test                       :    0.9924

Anderson-Darling statistic = A2       :    4.50
p-value of test                       :  5.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9972


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:01.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.48e-3
p-value of test                       :    0.9985

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:32.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.27e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.59e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:35.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:36.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.81
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.93
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.73
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.80
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:47.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.28
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.16
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:37.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.88
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.80
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17501.18
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.02
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.86
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.22
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.26
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.31
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.80
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.52
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.89
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.08
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.49
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.52
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.26
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.75
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.11
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.41
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.36
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.63
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.98
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.25
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.21
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.41
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4856.15
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.81
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.32
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.01
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.44
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.07
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.76
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.52
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:34.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.19
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:20.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.12
p-value of test                       :    0.9947


-----------------------------------------------
Normal statistic for number of jumps  :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.85e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.82e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.60
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.28
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.85
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:06.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10075.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9850.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:43.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.88
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.38
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:50.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.44
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11664.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11718.97
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.77
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000132292

Normal statistic for number of bits   :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.46
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000022636

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.02
p-value of test                       :    0.98

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:00.34

 All tests were passed




Server wird beendet - Lösche Semaphor 112132106.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:57.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:06.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:05.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:57.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:01.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    3.39
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    3.61
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:14.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:48.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   21.59
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.10
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.90
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.84
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.66
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.88
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.77
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.74
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:09.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7088.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.41
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.79
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:09.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.78
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.09
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:37.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5060.88
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45723
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869723
  j =  1                              :        399908556
  j =  2                              :            45719
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46100
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870100
  j =  1                              :        399907804
  j =  2                              :            46092
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:30.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:18.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9991    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:01.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:36.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.59e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:44.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:45.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.78
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.50
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.63
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.15
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.35
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.38
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.81
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17084.13
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.26
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.75
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.23
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.47
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.99
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.52
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.88
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.06
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.74
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.59
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.07
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.20
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.74
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.77
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.32
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.36
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.07
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.87
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.03
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.93
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4848.97
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.09
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.83
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.93
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.04
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.11
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.37
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.11
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.84
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.29
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    1.63
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.66e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 9.09e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.63e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.94
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.02
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.39
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:04.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:05.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9856.87
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10114.23
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:04:20.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:53.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.13
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:53.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3987.80
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11863.40
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11780.17
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.31
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000036208

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.89
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000007048

Normal statistic for number of bits   :   0.056
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.43

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.089
p-value of test                       :    0.46

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.92
p-value of test                       :    0.97

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:16.70

 All tests were passed




Server wird beendet - Lösche Semaphor 113082378.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1263
p-value of test                       :    0.9971

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334383
  j =  1                              :        599997474
  j =  2                              :             1263
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5376
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:55.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4138
p-value of test                       :    0.9988


-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:04.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:54.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7127
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:59.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:15.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    4.17
p-value of test                       :  7.3e-3

Stat. AD after spacings (mNP2-S)      :    4.22
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:02:48.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.14
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.28
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.80
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.97
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.67
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.98
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.43
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.46
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:02.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7029.49
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:03.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.32
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.60
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4835.04
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:57.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45654
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869654
  j =  1                              :        399908693
  j =  2                              :            45652
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46017
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870017
  j =  1                              :        399907972
  j =  2                              :            46005
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:27.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:17.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:59.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:33.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.21e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : 2.49e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:37.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.045
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:48.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.31
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.78
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:48.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.98
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.66
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.88
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:39.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.06
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   11.48
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.20e-5
p-value of test                       : 1 -  4.2e-5    *****

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  167.67
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17469.02
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.17
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.79
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.14
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.14
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.98
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.21
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.92
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.36
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.67
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.22
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.19
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.70
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.81
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.15
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.44
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.92
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.37
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.03
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.58
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:43.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.86
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.93
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.30
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.64
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.78
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.59
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.63
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.73
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.08
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.81
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:34.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.92
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:22.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.93
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:25.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 2.05e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.38e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.74
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.81
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.59
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:07.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.24
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:05.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9947.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9863.68
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:42.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.12
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:47.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.61
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:49.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.01
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.49
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11648.78
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11922.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.85
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000023299

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.04
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999960755

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:07.63

 All tests were passed




Server wird beendet - Lösche Semaphor 114032650.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5530
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:57.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:42.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:59.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:07.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:06.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:59.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:58.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:14.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9921

Test on the Nm values of W_{n,i}(mNP1):    2.37
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    6.42
p-value of test                       :  6.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:43.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.12
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.67
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.43
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.78
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.22
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.75
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.70
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.90
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.61
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:06.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7342.20
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.09
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:08.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.94
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.00
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5057.32
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:54.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45744
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869744
  j =  1                              :        399908520
  j =  2                              :            45728
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46301
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870301
  j =  1                              :        399907401
  j =  2                              :            46295
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:28.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:18.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:00.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.56e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.34
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.64
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.26
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.27
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.91
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17240.25
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.93
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.56
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.23
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.89
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.00
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.95
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.13
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.53
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.79
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.70
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.12
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.40
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.92
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.53
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.99
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.30
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.51
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.88
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.29
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4864.59
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.40
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.38
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:34.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.98
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.10
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4877.88
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.38
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.98
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:34.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.54
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:20.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.70
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.16e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 5.94e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.27e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.38
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.28
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:04.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.02
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9874.82
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:04:15.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5017.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:52.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4687.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:54.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11697.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:31.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11542.79
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.90
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000196732

Normal statistic for number of bits   :    1.56
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.85
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000081001

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:03.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP2S, t = 16        6.3e-4
 84  Fourier3, r = 0                 0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 115015690.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5555
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:54.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4242
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:57.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7470
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:05.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:05.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:55.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:00.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    2.57
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    2.39
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.01
p-value of test                       :  8.9e-3

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.13
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    2.05
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:16.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.68
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.91
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.58
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.88
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.82
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.42
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.49
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:45.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7058.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:43.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.67
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.96
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:04.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.28
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.43
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5027.53
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:54.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45933
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869933
  j =  1                              :        399908137
  j =  2                              :            45927
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45774
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869774
  j =  1                              :        399908453
  j =  2                              :            45772
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9916

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 8.00e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:27.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:18.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:47.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:02.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:33.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:33.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:48.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.68
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.33
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.21
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.36
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.80
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.72
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   98.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17191.53
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.27
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.39
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.80
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.25
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.76
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.21
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.62
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.32
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.55
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.61
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.41
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.32
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.89
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.57
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.17
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.93
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.55
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.94
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.90
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.96
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.58
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.41
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5112.09
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.48
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.75
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.58
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.83
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5112.68
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.78
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.10
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.09
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    1.74
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.68
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:24.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :  7.6e-3

Kolmogorov-Smirnov- statistic = D-    : 2.57e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.09e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 9.61e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.49
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.38
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:05.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:07.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9763.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10196.47
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:39.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4993.10
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:50.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12024.58
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12119.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.11
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999902051

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.97
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000008236

Normal statistic for number of bits   :   0.065
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:03.85

 All tests were passed




Server wird beendet - Lösche Semaphor 116097034.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:55.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:41.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:57.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7170
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:05.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:55.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:00.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    3.07
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:53.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.96
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.11
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.32
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:21.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:54.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.21
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.99
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.04
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.18
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.43
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.67
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  479.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:44.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1487.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:00.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7218.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:05.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.15
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.62
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:33.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5028.55
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:57.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46039
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870039
  j =  1                              :        399907927
  j =  2                              :            46029
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45694
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869694
  j =  1                              :        399908616
  j =  2                              :            45686
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:27.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 5.85e-3
p-value of test                       :    0.9931

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:17.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:55.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.85e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.55e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.067
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:36.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.58
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:47.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.24
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.33
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.32
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.12
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:39.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.75
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.54
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17665.46
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.76
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.39
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.52
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.92
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.78
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.81
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.36
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.68
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.33
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.84
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.50
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.47
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.35
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.52
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.92
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.61
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.67
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.91
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.06
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4913.99
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.41
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.54
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.89
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.89
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.04
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.90
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.97
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.72
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.59
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -1.65
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:22.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.11

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.68e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.96e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.11
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.26
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.03
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:04.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.59
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9780.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:40.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.13
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.47
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.54
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12153.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.03
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.19
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999983021

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.33
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999977105

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:33.85

 All tests were passed




Server wird beendet - Lösche Semaphor 117112842.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:56.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:41.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:57.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:06.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:57.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:02.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:18.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:46.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.18
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.56
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.23
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.83
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.66
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.80
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  369.65
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:44.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.17
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7196.60
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.71
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:05.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.54
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.47
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5183.90
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:57.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45897
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869897
  j =  1                              :        399908208
  j =  2                              :            45893
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45814
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869814
  j =  1                              :        399908379
  j =  2                              :            45800
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:27.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:34.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:33.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.68
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.54
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.44
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.65
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17402.42
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.19
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.90
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.95
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.87
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.08
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.89
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.34
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.94
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.13
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.69
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.51
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.61
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.37
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.23
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.26
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.53
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.45
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.35
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.16
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.44
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.51
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4873.46
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.83
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.63
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.09
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  472.18
p-value of test                       :  1.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.07
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.77
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.95
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.62
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :   -1.53
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:23.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.16
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    1.33
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:22.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 3.27e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.47e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.55
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.85
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.32
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.49
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:05.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10094.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9840.74
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:40.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.25
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:47.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5024.71
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:51.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.35
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11713.58
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11867.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.04
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999845015

Normal statistic for number of bits   :   -1.23
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.27
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999816146

Normal statistic for number of bits   :   -1.45
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.12

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:18.07

 All tests were passed




Server wird beendet - Lösche Semaphor 118095882.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5280
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:56.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:42.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:59.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:00.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:07.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:07.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:58.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:01.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    3.87
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     831
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.28
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:12.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:45.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.15
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.31
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.54
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.80
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.54
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1374.45
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:03.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.00
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.51
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:02.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.98
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.39
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:35.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5136.23
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:57.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46128
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870128
  j =  1                              :        399907749
  j =  2                              :            46118
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45529
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869529
  j =  1                              :        399908948
  j =  2                              :            45517
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:28.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:20.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 9.64e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 2.94e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.97
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.70
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.28
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.24
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:43.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.94
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.57
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.78
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.86
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17204.25
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.60
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.24
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.07
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.94
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.50
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.37
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.43
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.41
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.79
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.24
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.10
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.70
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.57
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.64
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.89
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.10
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.30
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.32
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.03
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.64
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.79
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4805.50
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.21
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.80
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.46
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.84
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5153.27
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.19
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.07
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.46
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:24.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.72
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :  -0.010
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:24.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.67e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 6.48e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.20e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.20
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.44
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.62
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:06.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.21
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9972.33
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.70
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:57.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:49.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.76
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:51.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.68
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4010.01
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11942.69
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11967.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.52
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999929441

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.74
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999971783

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:42.10

 All tests were passed




Server wird beendet - Lösche Semaphor 119111690.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1270
p-value of test                       :    0.9948

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334390
  j =  1                              :        599997460
  j =  2                              :             1270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:57.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:45.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:10.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:10.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:03.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     856
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.01
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    4.92
p-value of test                       :  3.1e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:15.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:49.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.18
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.13
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.61
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.05
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.25
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.64
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.48
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.55
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:49.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7071.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.67
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
p-value of test                       :    0.9912

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.65
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:11.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.13
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.98
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:37.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4967.94
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:11.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45943
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869943
  j =  1                              :        399908118
  j =  2                              :            45935
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46190
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870190
  j =  1                              :        399907626
  j =  2                              :            46178
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:30.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:05.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:55.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.33
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:01:44.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.36
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.13
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.19
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.12
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.08
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:08.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.97
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.83
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17254.65
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.79
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.27
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.80
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.71
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.60
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.65
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.30
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.07
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.03
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.55
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.79
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.43
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.06
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.31
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.31
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.85
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.26
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.32
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.39
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.33
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.13
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.93
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.73
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.17
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.32
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.12
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.57
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.06
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.23
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.06
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:24.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.40
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -1.00
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:24.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.75
p-value of test                       :    0.96

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.52e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.84
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.49
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.08
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:03.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.23e-4
p-value of test                       :    0.9991    *****

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  255.09
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:02:04.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.60
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.24
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:04:18.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4961.00
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:53.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:55.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3944.65
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4249.81
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11957.65
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11737.67
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.42
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000098086

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.75
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999894335

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   0.032
p-value of test                       :    0.49

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:03.51

 All tests were passed




Server wird beendet - Lösche Semaphor 120127498.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:56.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:05.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:56.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:00.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    2.40
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:17.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:51.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.83
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.46
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.70
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.96
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.61
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.41
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.28
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1466.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:01.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7249.01
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:43.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.64
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.01
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:05.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.61
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.78
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:33.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5081.11
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:57.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45811
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869811
  j =  1                              :        399908386
  j =  2                              :            45795
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46129
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870129
  j =  1                              :        399907747
  j =  2                              :            46119
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:27.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:18.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  8.1e-3

Kolmogorov-Smirnov- statistic = D-    : 4.66e-3
p-value of test                       :    0.9949

Anderson-Darling statistic = A2       :    3.78
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:54.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.98e-3
p-value of test                       :    0.9933

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:32.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.74e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 3.44e-4
p-value of test                       :  8.7e-3

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.81
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:48.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.20
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.64
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.70
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:39.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.77
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.098
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.2e-3

Kolmogorov-Smirnov- statistic = D-    : 2.14e-3
p-value of test                       :    0.9978

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   92.88
p-value of test                       :    0.9942

-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17252.18
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.74
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.47
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.03
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.35
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.62
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.86
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.46
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.63
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.73
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.11
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.19
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.59
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.47
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.56
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.70
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.17
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.01
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.67
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.89
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.92
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.54
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.32
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.77
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.07
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.76
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.32
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.87
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.43
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:20.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.65
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   0.039
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:20.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.78
p-value of test                       :    0.04

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.34e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 9.43e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.83
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.52
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.56
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.14
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:01.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9766.14
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:31.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.90
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:39.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3999.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4205.32
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.80
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.06
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.91
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000073003

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.72
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000093088

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.84

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:00:03.96

 All tests were passed




Server wird beendet - Lösche Semaphor 121274378.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:47.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1468
p-value of test                       :  2.8e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334588
  j =  1                              :        599997064
  j =  2                              :             1468
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1464
p-value of test                       :  3.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334584
  j =  1                              :        599997072
  j =  2                              :             1464
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:42.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:33.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:52.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:54.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:01.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:01.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7485
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:58.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.93
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     943
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.47
p-value of test                       :  5.4e-3

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:10.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:38.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.17
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.63
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.20
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.24
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.39
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.63
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.58
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.90
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.47
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1359.58
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6934.24
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:09.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.88
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.10
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5092.20
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:02.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46253
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870253
  j =  1                              :        399907495
  j =  2                              :            46251
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46116
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870116
  j =  1                              :        399907772
  j =  2                              :            46108
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:30.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:18.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:45.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:59.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:53.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:35.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.23e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:44.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.39
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.43
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.18
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.34
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.90
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:48.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.49
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.61
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:32.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17447.83
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.93
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.02
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.22
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.28
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.42
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.43
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.39
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.64
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.24
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.83
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  100.33
p-value of test                       :    0.9985


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.55
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.67
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.01
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.62
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.72
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.20
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.43
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.94
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.13
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.01
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.43
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.83
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.24
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.66
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.37
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.40
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.55
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.39
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    1.18
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:25.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.95
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -1.29
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:24.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 9.81e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.95e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 6.52e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.52
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.15
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.16
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:07.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.44
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:09.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.75
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10107.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:04:19.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.07
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:52.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4981.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:54.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11776.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:33.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11899.28
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:33.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.75
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000002035

Normal statistic for number of bits   :   0.016
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.70
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999927824

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.73
p-value of test                       :    0.04

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:16:05.79

 All tests were passed




Server wird beendet - Lösche Semaphor 101941259.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5486
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:47.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:38.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:36.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:03.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:03.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:56.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:59.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    5.52
p-value of test                       :  1.6e-3

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:13.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:45.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.32
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.98
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.68
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.57
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.54
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.94
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.48
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1503.97
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:05.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7020.60
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:51.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.83
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.86
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:15.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.35
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:46.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.16
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5138.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:57.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45625
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869625
  j =  1                              :        399908753
  j =  2                              :            45619
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46134
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870134
  j =  1                              :        399907734
  j =  2                              :            46130
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:28.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9996    *****

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:15.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:42.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:36.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.01e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.32e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.090
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:44.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.18
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.10
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.38
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.05
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.29
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.40
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.71
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.2e-3

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.48
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  164.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17496.20
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.23
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.60
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.68
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.21
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.99
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.40
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.98
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.76
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.73
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.50
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.20
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.18
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.80
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.64
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.67
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.08
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.64
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.48
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.46
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.24
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.36
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5080.17
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.68
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.26
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.42
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.62
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.87
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.28
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  152.86
p-value of test                       :    0.9944


-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.00
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:22.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.95
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:46.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 4.53e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.34
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.25
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.89
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:08.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.12
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:07.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.39
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.05
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.032
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.60
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:04:21.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:54.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4738.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.75
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.03
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12127.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11575.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.64
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999989630

Normal statistic for number of bits   :  -0.082
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.41
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999956012

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    2.65
p-value of test                       :  4.5e-3

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.51

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:32.37

 All tests were passed




Server wird beendet - Lösche Semaphor 103251979.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:48.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5323
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:47.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:38.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:37.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:55.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4448
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:02.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:02.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:58.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:04.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.81
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    2.34
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:50.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:14.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:42.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.41
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.10
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.48
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.50
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.47
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.94
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:02.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7110.35
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:52.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.10
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.44
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.48
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:37.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5090.65
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9969


-----------------------------------------------
CPU time used                    :  00:03:02.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908204
  j =  2                              :            45889
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46376
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870376
  j =  1                              :        399907252
  j =  2                              :            46368
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:28.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:17.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:43.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:35.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.20e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.95
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.66
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.53
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.78
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.08
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.11
p-value of test                       : 1 -  6.8e-5    *****

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.75
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.78
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:39.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17580.13
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.27
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.48
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.20
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.10
p-value of test                       :    0.9925


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   70.22
p-value of test                       :  5.5e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.97
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.92
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.80
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.98
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.04
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  172.51
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.46
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.36
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.06
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.36
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.68
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.50
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.81
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.52
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.41
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.42
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.71
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.65
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.80
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.59
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.23
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.26
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:25.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.20
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:25.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.49e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.98e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 9.82e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.62
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.93
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.88
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:06.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.91
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:07.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9846.19
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10253.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:04:23.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4773.12
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4957.05
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:54.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4255.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.44
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11657.94
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11719.48
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.53
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999950228

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.12
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999893240

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:30.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 H (L=50, r=25)      5.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 104464395.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:51.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5515
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:49.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:38.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:38.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:55.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:03.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7497
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:54.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:00.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    3.50
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     672
p-value of test                       :  2.0e-3

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.44
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:13.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.08
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    3.13
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:46.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.02
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.35
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.34
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.12
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  273.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.02
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.00
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7191.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:44.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.99
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.49
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:02.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.31
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.68
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:34.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5013.34
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:52.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45858
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869858
  j =  1                              :        399908288
  j =  2                              :            45850
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869769
  j =  1                              :        399908465
  j =  2                              :            45763
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:28.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:18.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 6.27e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:53.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.89e-3
p-value of test                       :    0.9934

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:39.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.84
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.19
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.55
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.94
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:42.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.44
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.56
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17085.54
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.13
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.38
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.92
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.46
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.63
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.14
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.20
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.94
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.96
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.75
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.59
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.82
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.72
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.18
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.89
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.44
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4761.56
p-value of test                       :    0.9922


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.00
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.64
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.40
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.07
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.02
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.32
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :  -0.060
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:24.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.00
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:26.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.51e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.72
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.89
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.51
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:06.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10085.29
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9760.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:58.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.43
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.54
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11892.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.69
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000029146

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.69
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000022333

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:09.78

 All tests were passed




Server wird beendet - Lösche Semaphor 105414667.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5518
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:53.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4224
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:10.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:10.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:10.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7150
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:15.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    3.26
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     975
p-value of test                       :  7.0e-3

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     644
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.45
p-value of test                       :  1.9e-3

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:14.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.61
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.10
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.38
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  190.38
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.47
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1474.44
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:01.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6890.49
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:55.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.29
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.77
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:20.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:46.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.13
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4973.39
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:17.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45803
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869803
  j =  1                              :        399908396
  j =  2                              :            45799
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45668
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869668
  j =  1                              :        399908665
  j =  2                              :            45666
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:31.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:20.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:10.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.21e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.021
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.41
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.76
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.73
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.83
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.83
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.26
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.20
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.79
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.29
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17402.01
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.46
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.96
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.91
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.34
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.42
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.56
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.31
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.84
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.85
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.24
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.26
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.59
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.95
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.79
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.28
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.25
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.03
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.11
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.19
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.26
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.96
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.59
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.56
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.32
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.01
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  453.96
p-value of test                       :  8.0e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.29
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.05
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.65
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.62
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:25.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.57
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:25.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.29e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.91e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.62
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.04
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9912

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.64
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:05.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:05.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10205.08
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10140.23
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:12.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.022
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:04:31.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.82
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:56.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.40
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:00.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.81
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:33.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11717.86
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:35.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.61
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000059755

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.64
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999956939

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:55.15

 All tests were passed




Server wird beendet - Lösche Semaphor 106332171.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5329
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:54.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:05.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:05.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:56.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:02.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    3.17
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     982
p-value of test                       :  3.7e-3

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    2.78
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:14.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:42.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.60
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.40
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.71
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.50
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.75
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.99
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.75
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.70
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  496.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1361.56
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:00.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6984.27
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.83
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:03.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.44
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.61
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4954.55
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:55.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45917
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869917
  j =  1                              :        399908169
  j =  2                              :            45911
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46163
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870163
  j =  1                              :        399907677
  j =  2                              :            46157
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:27.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:18.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:45.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  9.9e-3

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:54.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:35.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.87e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.68
p-value of test                       :  3.6e-3

-----------------------------------------------
CPU time used                    :  00:01:37.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:35.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.84
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.80
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.04
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.66
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.90
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.06
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.33
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17433.02
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.56
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.13
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.28
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.42
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.37
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.00
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.33
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.84
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.91
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.74
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.96
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  577.27
p-value of test                       :  9.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.86
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.67
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  188.41
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.49
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.35
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.96
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.62
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.18
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.77
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.82
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.73
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.43
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.05
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5119.48
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.24
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.28
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.73
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:23.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.20
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:24.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.87e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 9.88e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.17e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.64
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.01
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :  5.4e-4    *****

Anderson-Darling statistic = A2       :    4.04
p-value of test                       :  8.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  244.85
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:05.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.56
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10022.51
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9810.82
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:40.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4205.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.53
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11942.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12044.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.19
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999970670

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.88
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000017377

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.90
p-value of test                       :    0.03

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:56.88

 All tests were passed




Server wird beendet - Lösche Semaphor 107544587.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9904


-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5411
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:53.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:40.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:58.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:08.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7481
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:07.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:05.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:08.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    2.06
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:14.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:43.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.05
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.10
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.56
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.55
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.86
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.70
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1504.27
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:03.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7065.40
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.66
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.92
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:14.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.05
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.73
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:38.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.73
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:00.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45678
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869678
  j =  1                              :        399908646
  j =  2                              :            45674
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46114
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870114
  j =  1                              :        399907776
  j =  2                              :            46106
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:31.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:19.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:03.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 9.41e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:37.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.22e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.06e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 8.55e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.064
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:51.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:54.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.93
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.74
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.42
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.93
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:49.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.32
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.93
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17610.02
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.77
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.05
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.77
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.06
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.66
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.04
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.96
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.99
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.70
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.51
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.31
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.28
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.22
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.14
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.60
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.04
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.78
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.10
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.05
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.85
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.03
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.17
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.03
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.45
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.06
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.52
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.44
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.04
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.92
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    2.32
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:02:25.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.20
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:24.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.92e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.61e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.86
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.66
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.34
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:05.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.48
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9782.43
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.91
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:18.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.38
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.33
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:04.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.32
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4021.94
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11748.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:36.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11867.46
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:38.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.75
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000101143

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.35
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999781133

Normal statistic for number of bits   :   -1.73
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    2.50
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:45.89

 All tests were passed




Server wird beendet - Lösche Semaphor 108560395.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:03.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5409
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:53.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:07.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:08.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:01.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:06.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     969
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.18
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.55
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:14.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:41.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.74
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.77
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.34
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.75
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.49
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.63
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.46
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.63
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1364.14
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:04.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6897.60
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.61
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.97
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.19
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:10.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.02
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.16
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:37.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5159.56
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:56.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45544
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869544
  j =  1                              :        399908918
  j =  2                              :            45532
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45566
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869566
  j =  1                              :        399908871
  j =  2                              :            45560
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:28.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9929


-----------------------------------------------
CPU time used                    :  00:02:17.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:02.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 3.07e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:24.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.52
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.61
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.91
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.49
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.07
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:45.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.58
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.22
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.82
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17167.30
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.88
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.75
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    9.86
p-value of test                       :    0.9970


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.95
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.24
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.78
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.58
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.38
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.71
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.65
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.25
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.81
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.70
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.47
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.25
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.40
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.00
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.06
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.58
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.63
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.87
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4837.08
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.17
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.37
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.79
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.24
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4817.80
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.59
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.37
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.11
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:22.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.71
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.78e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 8.25e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.09
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.84
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.37
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:04.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:04.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10090.78
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.68
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:58.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5071.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:51.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4328.03
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.27
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.64
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12101.54
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:30.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.30
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999849119

Normal statistic for number of bits   :   -1.19
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.72
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999898490

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :  -0.044
p-value of test                       :    0.52

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.91

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :  -0.031
p-value of test                       :    0.51

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:20.09

 All tests were passed




Server wird beendet - Lösche Semaphor 109543435.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:53.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4435
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7101
p-value of test                       :    0.9945


-----------------------------------------------
CPU time used                    :  00:03:11.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:09.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:11.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.21
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     854
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.01
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    2.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:14.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:43.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.30
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.48
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.92
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.76
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.73
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.30
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.16
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.63
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:54.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:07.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6890.76
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:57.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.53
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:13.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.17
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.46
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5111.37
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:56.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45980
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869980
  j =  1                              :        399908044
  j =  2                              :            45972
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908188
  j =  2                              :            45903
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:32.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:21.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:50.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:07.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:38.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.91e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.51e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.064
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.99
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.81
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.94
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.91
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.62
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:50.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.59
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.07
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   17.19
p-value of test                       :  6.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17624.36
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.38
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.83
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.97
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.47
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.78
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.08
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.47
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.66
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.78
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.18
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.09
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.87
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.01
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.56
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.42
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  101.91
p-value of test                       :    0.9979


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.38
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.27
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.32
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.11
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.10
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.24
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.14
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.57
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  307.34
p-value of test                       :    0.9984


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.09
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5181.16
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.08
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.23
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.69
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:23.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.09
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    1.16
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.00e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.02e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.77
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.96
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.32
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:04.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.11
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:03.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10129.13
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.33
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:04:13.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.98
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:53.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4786.74
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.39
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4270.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11606.30
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.15
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.98
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999945386

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.50
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999903770

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.87
p-value of test                       :    0.97

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:10.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 69  MatrixRank, L=1000, r=26        6.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 110624779.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:09.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5381
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:54.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7151
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:57.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:05.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:05.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:56.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    2.91
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     986
p-value of test                       :  2.5e-3

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    2.50
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.85
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:16.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:49.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.64
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.23
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.83
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.77
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.92
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  192.08
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.16
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:43.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.88
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7067.86
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.98
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.01
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:04.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.75
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   83.91
p-value of test                       :    0.9938


-----------------------------------------------
CPU time used                    :  00:01:34.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4914.43
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:57.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46047
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870047
  j =  1                              :        399907908
  j =  2                              :            46043
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46169
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870169
  j =  1                              :        399907664
  j =  2                              :            46165
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.65e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.76
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  4.2e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    4.03
p-value of test                       :  8.6e-3


-----------------------------------------------
CPU time used                    :  00:02:28.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:17.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:45.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:59.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:38.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.02
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.48
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.49
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.46
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.84
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.87
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.79
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-3
p-value of test                       :    0.9988

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :  8.3e-4    *****

Anderson-Darling statistic = A2       :    5.06
p-value of test                       :  2.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :18000.16
p-value of test                       :  1.2e-3



-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.22
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.58
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.34
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.65
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.33
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.15
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.47
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.48
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.98
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.78
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.71
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.02
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.19
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.90
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.10
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.96
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.60
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.44
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.70
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  460.16
p-value of test                       :  4.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  324.94
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.66
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.98
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.42
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.76
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.03
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.05
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.93
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.96
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.94
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:23.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.78
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.033
p-value of test                       :    0.49

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 3.41e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.69
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.13
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.83
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:03.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:04.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.89
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9926

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.70
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.022
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:35.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4994.97
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5038.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:49.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.70
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11930.41
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11780.17
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.27
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999954131

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.48
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999990035

Normal statistic for number of bits   :  -0.079
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9906

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :  -0.025
p-value of test                       :    0.51

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.63
p-value of test                       :    0.05

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:51.93

 All tests were passed




Server wird beendet - Lösche Semaphor 111673355.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:49.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5608
p-value of test                       :  5.9e-3


-----------------------------------------------
CPU time used                    :  00:03:56.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:43.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:01.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:12.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:12.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:57.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:01.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     972
p-value of test                       :  9.2e-3

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:17.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    2.13
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:47.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.80
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.63
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.17
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.92
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.06
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:31.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.21
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:27.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.48
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:15.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7052.61
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:33.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.92
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:05.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.78
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.87
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:33.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4993.13
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:00.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45796
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869796
  j =  1                              :        399908410
  j =  2                              :            45792
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45886
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869886
  j =  1                              :        399908230
  j =  2                              :            45882
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:30.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:19.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.9e-3

Kolmogorov-Smirnov- statistic = D-    : 1.99e-3
p-value of test                       :    0.9979

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:34.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.01e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.92e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:39.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.01
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.22
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.79
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:59.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.86
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.95
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.080
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.30
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17314.84
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.12
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.93
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.29
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.13
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.13
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.39
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.97
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.71
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.22
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.95
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.66
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.20
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.86
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.47
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.95
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.11
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.34
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.60
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.85
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4853.39
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.47
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.64
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.70
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.23
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.16
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.67
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.71
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:34.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.96
p-value of test                       :  7.8e-3


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:22.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.26
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:22.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 4.15e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.82
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.08
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.16
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.41
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:08.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9784.87
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9819.16
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:35.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.40
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.42
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:50.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.02
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.53
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11699.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11988.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.62
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000078733

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.70
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000084460

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:39.45

 All tests were passed




Server wird beendet - Lösche Semaphor 112689163.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5405
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:55.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:41.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4435
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:05.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:05.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:01.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     947
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:16.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:43.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.13
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.24
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.36
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.52
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.20
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.24
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.51
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.29
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:45.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.07
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6844.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:40.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.77
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.68
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:04.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.63
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.78
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4804.18
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:59.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45843
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869843
  j =  1                              :        399908319
  j =  2                              :            45833
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45931
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869931
  j =  1                              :        399908142
  j =  2                              :            45923
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :  3.8e-3

Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
p-value of test                       :    0.9922

Anderson-Darling statistic = A2       :    4.49
p-value of test                       :  5.1e-3


-----------------------------------------------
CPU time used                    :  00:02:18.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:59.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.35e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 8.33e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.02
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   38.82
p-value of test                       :    0.9977

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.06
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   63.51
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.40
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:38.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.93
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.17
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.77
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17302.29
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.22
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.96
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.86
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.75
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.00
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.94
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.83
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.32
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.93
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.44
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.28
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.50
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.11
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.27
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.22
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.28
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.35
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.67
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.64
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.85
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.25
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5214.38
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.79
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.62
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.40
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.49
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.56
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.38
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.74
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.84
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.83
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -2.14
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:23.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 7.36e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 8.87e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.81
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.98
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.90
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:03.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.36
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:03.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10070.05
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10160.32
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.052
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:39.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.13
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4675.59
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3853.16
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.11
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11781.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11785.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.50
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000090037

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.51
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000037960

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:41.42

 All tests were passed




Server wird beendet - Lösche Semaphor 113672203.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.83

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5528
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:54.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7469
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:41.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:06.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:05.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:56.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:02.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.32
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.97
p-value of test                       :  9.2e-3

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    2.37
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:13.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:43.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.91
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.59
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.82
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.82
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.10
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.19
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.40
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.56
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:01.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6898.44
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.78
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:04.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.09
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.89
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5082.13
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  5.5e-3


-----------------------------------------------
CPU time used                    :  00:02:55.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908202
  j =  2                              :            45893
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45765
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869765
  j =  1                              :        399908476
  j =  2                              :            45753
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:27.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:18.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:33.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 5.54e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.98
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.62
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.61
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.66
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.14
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:39.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.85
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.95
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17409.52
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.88
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.26
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.97
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.59
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.44
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.52
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.12
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.34
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.55
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.54
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.92
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.59
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  103.63
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.39
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.06
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.65
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.12
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.61
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.58
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.41
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.88
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.61
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.56
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.56
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.25
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.08
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.44
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.56
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:24.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.95
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :  -0.019
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:24.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.73
p-value of test                       :    0.04

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.96e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.25
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.36
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.90
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:05.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.65
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:05.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10132.24
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10249.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:37.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.17
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:47.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4747.96
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:49.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4252.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4194.74
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11940.95
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11853.99
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.67
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000052642

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.08
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000016219

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         : 7.70e-3
p-value of test                       :    0.50

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:28.70

 All tests were passed




Server wird beendet - Lösche Semaphor 114655243.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1247
p-value of test                       :    0.9993    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334367
  j =  1                              :        599997506
  j =  2                              :             1247
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5302
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:52.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:58.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:06.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:05.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7149
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:57.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:03.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.30
p-value of test                       :  6.4e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    3.77
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:14.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    2.80
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:43.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.53
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.27
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.99
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  264.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.89
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:02.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7184.59
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.23
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.39
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:03.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.38
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.74
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:32.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4896.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:00.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45826
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869826
  j =  1                              :        399908353
  j =  2                              :            45816
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45646
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869646
  j =  1                              :        399908710
  j =  2                              :            45642
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:26.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:17.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:01:34.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.39e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.091
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:34.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.22
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.61
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.06
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.14
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.63
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:40.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.43
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :  1.0e-3

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17574.06
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.80
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.04
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.99
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.81
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.39
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.92
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.20
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.91
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.35
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.38
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.46
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.91
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.29
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.57
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.82
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.21
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.66
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.72
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.19
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.47
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.17
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.66
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.94
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:34.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.84
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.56
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4900.11
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.28
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.77
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:34.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.84
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:23.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.92
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    1.65
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 9.43e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.10e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.26
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.37
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.09
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.72
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:06.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.77
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.051
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:37.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.00
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4754.96
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4299.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11968.65
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12034.17
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.06
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000094498

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.65
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999996902

Normal statistic for number of bits   :  -0.024
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :  -0.032
p-value of test                       :    0.51

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   0.057
p-value of test                       :    0.48

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:36.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14           0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 115671051.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5533
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:53.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:08.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7118
p-value of test                       :    0.9905


-----------------------------------------------
CPU time used                    :  00:03:07.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:59.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:03.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    3.09
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     845
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:13.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9923

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:41.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.52
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.04
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.58
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.98
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.16
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.24
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  273.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.53
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1377.66
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6867.78
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.08e-3
p-value of test                       :    0.9969

Kolmogorov-Smirnov- statistic = D-    :    0.79
p-value of test                       :  3.8e-4    *****

Anderson-Darling statistic = A2       :    5.77
p-value of test                       :  1.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   59.78
p-value of test                       :  9.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.87
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:08.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.95
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.28
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4944.81
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:00.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45602
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869602
  j =  1                              :        399908798
  j =  2                              :            45598
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45840
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869840
  j =  1                              :        399908324
  j =  2                              :            45832
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:30.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:19.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:06.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.05e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.57
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.30
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   39.03
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.38
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.99
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.20
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.13
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.32
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17234.07
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.89
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.02
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.34
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.92
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.70
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.82
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.26
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.90
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.56
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.72
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.96
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.36
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.02
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.66
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.24
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.37
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.81
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.09
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.55
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.30
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.46
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.20
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.39
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.21
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.31
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4931.12
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.01
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.51
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -1.73
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:23.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.13
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    1.34
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:24.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.06e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.37e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.63
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.44
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.91
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:05.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.11
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:03.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9935

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9943.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9816.12
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:04:13.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:51.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.51
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:53.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.25
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.20
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11956.57
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11462.67
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.10
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999986306

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.13
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000099163

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.02e-4
p-value of test                       :    0.9991    *****

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.25
p-value of test                       :    0.01

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:08.02
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 38  Run, r = 0                      9.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 116588555.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:55.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:58.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:06.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:06.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:58.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:03.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     948
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:13.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    2.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:38.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.70
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.49
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.77
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.95
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.08
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.87
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1494.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7083.61
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.75
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.83
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.13
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.52
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:32.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5115.30
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:56.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45678
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869678
  j =  1                              :        399908650
  j =  2                              :            45666
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46048
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870048
  j =  1                              :        399907910
  j =  2                              :            46036
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:27.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:17.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.91e-3
p-value of test                       :    0.9921

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:59.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:57.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:34.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.19e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.62e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:35.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.43
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.56
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   62.15
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.31
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:37.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.43
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.98
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.62
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17225.30
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.84
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.12
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.36
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.55
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.42
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.15
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.50
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.82
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.76
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.36
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.82
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.82
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.87
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  103.72
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.15
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.99
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.72
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.50
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.83
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.22
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.94
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.45
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  319.69
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.80
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.97
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.86
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.52
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.91
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.63
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.93
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    1.60
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:23.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.57
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.07e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.46e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.27
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.32
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.97
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.78
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:04.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9811.88
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.93
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:36.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.03
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4299.64
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4025.39
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11737.27
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12119.35
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.14
p-value of test                       :  9.9e-3


-----------------------------------------------
Total number of bits:  8000206359

Normal statistic for number of bits   :    1.63
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.96
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000148873

Normal statistic for number of bits   :    1.18
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:29.29

 All tests were passed




Server wird beendet - Lösche Semaphor 117571595.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5427
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:55.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:45.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:01.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:12.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:11.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:08.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:12.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     844
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.47
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.47
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    2.43
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     253
p-value of test                       :    0.9970

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:14.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:42.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.01
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.37
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.19
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.93
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.33
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.85
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.27
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.36
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:56.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1516.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:03.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7134.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.70
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.85
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:17.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.65
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.85
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5059.20
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:57.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45979
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869979
  j =  1                              :        399908048
  j =  2                              :            45967
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908181
  j =  2                              :            45908
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:32.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  8.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9943


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:21.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:54.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:12.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:58.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.056
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:53.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.85
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.85
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.02
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   47.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:53.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.03
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.00
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    4.24
p-value of test                       :  7.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   92.13
p-value of test                       :    0.9951

-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17544.85
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.54
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.90
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.77
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.05
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   40.60
p-value of test                       :  1.1e-3


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.56
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.62
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.65
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.22
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.68
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.60
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.71
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.63
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.22
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.71
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.33
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  440.68
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.25
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.63
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.03
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.17
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.54
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.07
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.03
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.48
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.92
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.71
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.06
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.16
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.23
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:21.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.47
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:22.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.68e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.51e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.81
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.54
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.97
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:04.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.40
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:04.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10227.14
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9798.84
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:04:27.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.93
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.06
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.46
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3987.61
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11766.71
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11776.87
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:38.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.40
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000245566

Normal statistic for number of bits   :    1.94
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.64
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000122311

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:01.59

 All tests were passed




Server wird beendet - Lösche Semaphor 118587403.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:48.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5290
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:55.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4445
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7500
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:04.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:05.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:02.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:16.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.21
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9962

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    2.28
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:46.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.19
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.47
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.13
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.69
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  269.01
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.28
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:43.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.64
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:00.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6850.92
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:42.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.39
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:03.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.03
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.97
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5109.73
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:00.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45788
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869788
  j =  1                              :        399908427
  j =  2                              :            45782
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46339
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870339
  j =  1                              :        399907325
  j =  2                              :            46333
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:28.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 9.69e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:18.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:59.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 7.79e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 9.15e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.24
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.63
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.91
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:48.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.47
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.61
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   47.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.86
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.00
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.10
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.24
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.90
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17618.25
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.35
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.89
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.93
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.22
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.19
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.77
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.60
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.24
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.44
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.31
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.17
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.96
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.36
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.68
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.47
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.09
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.57
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.49
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.33
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4818.67
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.15
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.31
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.35
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.06
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.76
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.43
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.73
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.72
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:22.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.37
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    1.48
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:21.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.80e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.17
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.55
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.86
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:04.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.61
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:03.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 8.76e-3
p-value of test                       :    0.9905

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9674.57
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9812.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:41.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.38
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.04
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:50.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4024.62
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.44
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11644.63
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11612.11
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.60
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999889826

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.28
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000119644

Normal statistic for number of bits   :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:32.84

 All tests were passed




Server wird beendet - Lösche Semaphor 119668747.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5524
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:57.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:04.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:55.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:00.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.70
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:15.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    3.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:46.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.21
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.65
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.89
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.63
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7037.57
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.88
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.53
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:04.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.51
p-value of test                       :    0.9918


-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.29
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5174.70
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:00.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45589
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869589
  j =  1                              :        399908825
  j =  2                              :            45583
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46087
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870087
  j =  1                              :        399907831
  j =  2                              :            46077
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.79
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:28.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-3
p-value of test                       :    0.9989

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  1.8e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:19.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.90e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.41
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.35
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:47.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.27
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.20
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:37.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.26
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.08
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17528.94
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.05
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.74
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.50
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.72
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.53
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.13
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.09
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.11
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.43
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.45
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.60
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.06
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.73
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.17
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.04
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.05
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.10
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.48
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.21
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.63
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.14
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.80
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.17
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.44
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.87
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.58
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  159.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.73
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:22.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.39
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    1.48
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.37e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 6.77e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.09
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.05
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:03.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.75
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:04.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10206.63
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9901.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:42.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:50.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3974.91
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4268.39
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11790.47
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11818.74
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:29.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.47
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999890177

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.95
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000112738

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
p-value of test                       :    0.9915

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.86
p-value of test                       :    0.03

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    2.85
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:17.19

 All tests were passed




Server wird beendet - Lösche Semaphor 120684555.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:48.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5483
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:04.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7164
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:04.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:55.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:01.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    2.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    3.54
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     353
p-value of test                       :  1.5e-3

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:11.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.61
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.25
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.90
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.01
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.24
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.48
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:44.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1324.88
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7138.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:41.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.63
p-value of test                       :  9.1e-3

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.47
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:03.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.21
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   93.68
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:33.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5037.50
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:56.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45941
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869941
  j =  1                              :        399908119
  j =  2                              :            45939
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46204
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870204
  j =  1                              :        399907597
  j =  2                              :            46194
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:28.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:17.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:45.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:01.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:53.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :  1.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    3.60
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:33.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 5.86e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:31.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.16
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.72
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.90
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.89
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.00
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.00
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.23
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.60
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.31
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17278.46
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.29
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.34
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.40
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.89
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.21
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.56
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.36
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.56
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.93
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.28
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.69
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.26
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.64
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.01
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.11
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.93
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.31
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.47
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.22
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.28
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:40.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.58
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.65
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5189.64
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.49
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.15
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.12
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.67
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.31
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.17
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.26
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.15
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:12.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.96
p-value of test                       :  5.6e-3


-----------------------------------------------
Normal statistic for number of jumps  :   -1.56
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:12.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 6.60e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.52e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.64
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.96
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.56
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:55.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.09
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10059.60
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:18.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4717.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4760.70
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.47
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.13
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11563.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.35
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000177085

Normal statistic for number of bits   :    1.40
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.25
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000051430

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.68

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:56:29.79

 All tests were passed




Server wird beendet - Lösche Semaphor 121634827.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5373
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:42.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:33.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:53.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:54.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:01.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:01.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:55.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:58.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.12
p-value of test                       :    0.9998    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:08.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     126
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:37.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.15
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.46
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.80
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.43
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.48
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.14
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1398.77
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:05.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7150.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.27
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:09.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.77
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.56
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5017.98
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:31.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46019
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870019
  j =  1                              :        399907966
  j =  2                              :            46011
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46091
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870091
  j =  1                              :        399907822
  j =  2                              :            46083
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:29.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:18.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:53.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.44e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.93e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:43.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:45.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.10
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.17
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.62
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.80
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.67
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.05
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.60
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:31.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:32.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.86
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.59
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17866.99
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.44
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.01
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.65
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.48
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.26
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.96
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.14
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.45
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.39
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.28
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.80
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.83
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.03
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.64
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.09
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.60
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.32
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.25
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.76
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5137.69
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.01
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.56
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.37
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.60
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.91
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.38
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.81
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:26.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.17
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:26.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 2.74e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.33
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.24
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.84
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.00
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:08.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:04:17.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.56
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:52.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5027.49
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:53.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4243.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11701.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:32.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11695.36
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:32.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.56
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999897617

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.90
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000235981

Normal statistic for number of bits   :    1.87
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    2.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:17:08.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP1, t = 3          0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 101974028.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:55.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5491
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:46.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:37.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:36.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:54.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:02.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:02.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:53.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:57.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:14.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.54
p-value of test                       :  5.3e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):   0.099
p-value of test                       : 1 -  2.3e-5    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:41.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.18
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.20
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.78
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.33
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.37
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.58
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.22
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.13
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.95
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1503.08
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6869.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:42.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.28
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.79
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:03.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.59
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.16
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5059.72
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:06.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45908
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869908
  j =  1                              :        399908187
  j =  2                              :            45902
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45951
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869951
  j =  1                              :        399908104
  j =  2                              :            45939
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:27.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:17.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:54.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.45e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:32.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:33.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:47.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.83
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.23
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.57
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9929

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.71
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17526.37
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.20
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.74
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.27
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.97
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.57
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.19
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.66
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.71
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.70
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.56
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.98
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.86
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.95
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.67
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.79
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.68
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.08
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.34
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.40
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.74
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.74
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4871.27
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.45
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  162.01
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.78
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.26
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.44
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.53
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.23
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.77
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -1.36
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:25.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.21
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:27.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.64
p-value of test                       :  8.9e-5    *****

Kolmogorov-Smirnov- statistic = D-    : 2.41e-3
p-value of test                       :    0.9975

Anderson-Darling statistic = A2       :    6.92
p-value of test                       :  4.0e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -3.65
p-value of test                       :    0.9999    *****

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:46.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.62e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 3.82e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.29
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.40
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:06.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:09.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.80
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:39.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.30
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :  5.1e-4    *****

Anderson-Darling statistic = A2       :    5.02
p-value of test                       :  3.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5159.54
p-value of test                       :  3.6e-3

-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4194.33
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11959.16
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11735.31
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.13
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000073525

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.75
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000123217

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:33.84
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP1, t = 16        1 -  2.3e-5
 82  LempelZiv, r = 0                0.9999 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 103219212.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5442
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:47.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:38.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:36.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:54.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4173
p-value of test                       :    0.9937


-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:02.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:02.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:52.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:57.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:51.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:18.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:48.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.17
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.22
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.13
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.24
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.75
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1381.95
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:58.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7085.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.53
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.99
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:02.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.11
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.60
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:35.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4937.71
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46378
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870378
  j =  1                              :        399907249
  j =  2                              :            46368
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45846
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869846
  j =  1                              :        399908313
  j =  2                              :            45836
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9978


-----------------------------------------------
CPU time used                    :  00:02:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:54.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:01:33.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.95e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 8.40e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.43
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.71
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.07
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.35
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.46
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17569.95
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.77
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.85
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.83
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.54
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.81
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.97
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.31
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.05
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.72
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.96
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.56
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  179.58
p-value of test                       :  7.3e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.23
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.50
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.37
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.75
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.19
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.04
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  459.16
p-value of test                       :  5.0e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.01
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.46
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.62
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.28
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.84
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.32
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5138.93
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.83
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.64
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.64
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:24.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.76
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:25.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.33e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.31e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.26
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.78
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.25
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:06.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.02
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:09.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9764.30
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10149.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:41.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.56
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4717.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.95
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4196.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11694.64
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11711.79
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:30.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.83
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999910145

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.10
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000089794

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:29.03

 All tests were passed




Server wird beendet - Lösche Semaphor 104169484.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9932


-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1251
p-value of test                       :    0.9990    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334371
  j =  1                              :        599997498
  j =  2                              :             1251
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:47.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:37.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:37.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:55.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:02.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:01.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:52.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:57.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.95
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    2.65
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:12.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    3.75
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.17
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.69
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.63
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.75
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   85.12
p-value of test                       :  4.4e-3

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.02
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.48
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.64
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:52.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.73
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7118.48
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.06
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.35
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:02.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.19
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.49
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:35.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5081.12
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:55.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46034
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870034
  j =  1                              :        399907935
  j =  2                              :            46028
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45835
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869835
  j =  1                              :        399908332
  j =  2                              :            45831
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:28.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:59.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:03.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 9.67e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.023
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:31.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:47.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.27
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.37
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.95
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.86
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.85
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17408.59
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.67
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.47
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.16
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.17
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.71
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.78
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.88
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.80
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.72
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.01
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.16
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.34
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.14
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.75
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.72
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.63
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.18
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.44
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.06
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.54
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.54
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.84
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.32
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.37
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  451.18
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.30
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4897.37
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.19
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.97
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:34.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.28
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:23.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.25
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   0.021
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:24.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.95e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 8.14e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.03
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.71
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.40
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:06.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.71
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:09.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9969.44
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9835.93
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.047
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:39.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.81
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:51.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.96
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4271.74
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11779.12
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.77
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000022294

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.71
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000078316

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.22
p-value of test                       :    0.01

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.58e-3
p-value of test                       :    0.9963

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.16
p-value of test                       :    0.98

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.0e-3

Kolmogorov-Smirnov- statistic = D-    : 5.32e-4
p-value of test                       :    0.9995    *****

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.78
p-value of test                       :    0.9973

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:41.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  6  CollisionOver, t = 3            0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 105086988.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9976


-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1462
p-value of test                       :  4.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334582
  j =  1                              :        599997076
  j =  2                              :             1462
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5505
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:48.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:37.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:36.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:55.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:02.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:02.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:51.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:56.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.02
p-value of test                       :  8.6e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     955
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:12.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:43.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   19.18
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.87
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.42
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.08
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  197.40
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.79
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.84
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:58.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6995.44
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:42.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.43
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.49
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:03.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.80
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.73
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:34.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5073.55
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:54.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45927
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869927
  j =  1                              :        399908152
  j =  2                              :            45915
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45822
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869822
  j =  1                              :        399908358
  j =  2                              :            45818
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:28.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:18.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:33.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:33.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:47.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.47
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.84
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.96
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:38.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.00
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.07
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.12
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17516.06
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.78
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.37
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.66
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.30
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.82
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.90
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.99
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.18
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.68
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.49
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.60
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.52
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.28
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.97
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.02
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.88
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.38
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.48
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.08
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  119.34
p-value of test                       :  6.6e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.45
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4889.69
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.79
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  161.04
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.43
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.63
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.77
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.26
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.79
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.75
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:25.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.52
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:24.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.34e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.84e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.00e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.32
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.13
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.51
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:04.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.57
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:08.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10244.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:41.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.28
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:50.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.38
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.61
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11963.85
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12022.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.60
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999873449

Normal statistic for number of bits   :   -1.00
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.08
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000039694

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :  -0.099
p-value of test                       :    0.54

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    2.54
p-value of test                       :  6.6e-3

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:13.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 C (L=1000, r=20)    6.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 105938956.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5330
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:49.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:37.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:04.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:52.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:57.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.07
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.08
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.19
p-value of test                       :  7.2e-3

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    2.90
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:12.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:38.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.33
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.55
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.01
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.79
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.61
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.04
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:45.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.35
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:00.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7116.56
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:41.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.39
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.88
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:03.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.33
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.38
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:33.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5155.27
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:55.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45692
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869692
  j =  1                              :        399908616
  j =  2                              :            45692
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45745
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869745
  j =  1                              :        399908511
  j =  2                              :            45743
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:29.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:18.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.24e-3
p-value of test                       :    0.9930

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:34.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 3.16e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.96e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:33.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:48.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.17
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.23
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.12
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:47.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.85
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.00
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17568.07
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.25
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.39
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.45
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.25
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.50
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.83
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.39
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.71
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.85
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.57
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.98
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.58
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.81
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.17
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.35
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.81
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.60
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.68
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.38
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.68
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.40
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.77
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.39
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.33
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.90
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.36
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.39
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.08
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.50
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:22.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.97
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:24.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.16e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.83e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 9.18e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.27
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.84
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.58
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:05.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.65
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:07.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9872.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.54
p-value of test                       :    0.9944

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.081
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:45.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.82
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4691.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4179.65
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3999.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11647.27
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12233.00
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:01:29.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.85
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999989972

Normal statistic for number of bits   :  -0.079
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.24
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999968519

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.87
p-value of test                       :    0.97

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:35.81

 All tests were passed




Server wird beendet - Lösche Semaphor 106921996.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:50.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:52.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:38.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:38.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4181
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:05.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:05.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:57.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:59.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.52
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    2.35
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    4.43
p-value of test                       :  5.4e-3

-----------------------------------------------
CPU time used                    :  00:02:11.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:42.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.14
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.33
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.28
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.17
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.13
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.21
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.33
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.05
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:05.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7170.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.15
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:13.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.03
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.04
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5073.65
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:54.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46041
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870041
  j =  1                              :        399907919
  j =  2                              :            46039
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45813
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869813
  j =  1                              :        399908383
  j =  2                              :            45795
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:31.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:19.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.03e-3
p-value of test                       :    0.9907

Anderson-Darling statistic = A2       :    4.01
p-value of test                       :  8.8e-3


-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.84e-3
p-value of test                       :    0.9959

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:08.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:57.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:38.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.071
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.054
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.086
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:46.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.84
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.56
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.30
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.36
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.73
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.40
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.88
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.94e-5
p-value of test                       : 1 -  1.0e-4    *****

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    4.31
p-value of test                       :  6.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   81.93
p-value of test                       :  1.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.02
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17652.47
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.61
p-value of test                       :    0.9957


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.58
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.08
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.96
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.37
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.16
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.73
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.04
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.43
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.88
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.09
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.80
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.98
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.40
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.74
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  581.83
p-value of test                       :  6.6e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.14
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.13
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.03
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.04
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.14
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.60
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.90
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.91
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.67
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.80
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.82
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.64
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:21.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.34
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.23e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 5.44e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.51
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.99
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.00
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:05.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10161.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:04:27.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.49
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4985.26
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3977.08
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.80
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11567.15
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.02
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000118423

Normal statistic for number of bits   :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.07
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000185953

Normal statistic for number of bits   :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9912

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:15.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.05

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:42.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 67  MatrixRank, L=30, r=26          1.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 107905036.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:51.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:39.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:39.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:03.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7551
p-value of test                       :  3.5e-3


-----------------------------------------------
CPU time used                    :  00:03:02.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:54.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:04:00.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.61
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.21
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:13.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.74
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.14
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.80
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.80
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.84
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.32
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.78
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7199.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.46
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.78
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.25
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:32.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4766.24
p-value of test                       :    0.9971


-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:53.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45842
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869842
  j =  1                              :        399908321
  j =  2                              :            45832
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45644
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869644
  j =  1                              :        399908716
  j =  2                              :            45636
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:27.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:18.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.9e-3

Kolmogorov-Smirnov- statistic = D-    : 9.43e-4
p-value of test                       :    0.9990    *****

Anderson-Darling statistic = A2       :    6.73
p-value of test                       :  4.7e-4    *****


-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.12e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:31.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:31.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.32
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.35
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.71
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.60
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.64
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.62
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.34
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17389.92
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.93
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.62
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.48
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.80
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.61
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.99
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.48
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.61
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.05
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.35
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.09
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.63
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.64
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   47.11
p-value of test                       :    0.9938


-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.55
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.51
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.65
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.73
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.66
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.84
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.04
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5092.18
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  437.48
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.18
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.99
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.31
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.93
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.65
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.85
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.92
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:23.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.97
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:24.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.08e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 4.56e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.31
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.13
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:07.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.22
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.58
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10092.19
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:39.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.61
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.89
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4324.56
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11926.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12016.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.45
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999979097

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.76
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000059974

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    2.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:20.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 48  MaxOft AD, t = 24               4.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 109019148.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5509
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:49.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:39.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:38.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:04.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:53.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:00.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    2.13
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     957
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9929

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:12.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:40.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.41
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.06
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.71
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.47
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.02
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.91
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1345.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:59.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7240.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:41.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.50
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.41
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:04.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.77
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  158.87
p-value of test                       :  8.6e-3


-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5098.38
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:58.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45950
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869950
  j =  1                              :        399908104
  j =  2                              :            45942
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45942
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869942
  j =  1                              :        399908122
  j =  2                              :            45930
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:28.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:18.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.45e-3
p-value of test                       :    0.9947

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:33.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 6.36e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.33e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:32.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.33
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:48.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.05
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.62
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.53
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.49
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.51
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:38.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.98
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.52
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17184.09
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.20
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.76
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.17
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.05
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.45
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.40
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.91
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.89
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.27
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.74
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.97
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.41
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.46
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.80
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.95
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.26
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.40
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.08
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.83
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.65
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.63
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.83
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.91
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.05
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  456.77
p-value of test                       :  6.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4900.97
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.57
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.56
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.55
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   0.070
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:23.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.01
p-value of test                       :    0.9994    *****


-----------------------------------------------
Normal statistic for number of jumps  :   0.075
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:24.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.91e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 6.90e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.04e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.23
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.29
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:05.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:06.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10152.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.08
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.27
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:42.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.63
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.30
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.72
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4198.65
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11718.09
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11752.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.22
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000010060

Normal statistic for number of bits   :   0.080
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.93
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000126103

Normal statistic for number of bits   :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.00
p-value of test                       :    0.98

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:52.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 81  LinearComp, r = 0               0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 109969420.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5330
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:52.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:40.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:05.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:04.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:54.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:00.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.49
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9934

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:12.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:41.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.39
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.65
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.39
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.41
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.40
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  363.37
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.35
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:02.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7181.87
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.92
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:07.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.42
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.11
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:32.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5069.73
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:57.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45895
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869895
  j =  1                              :        399908211
  j =  2                              :            45893
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45883
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869883
  j =  1                              :        399908240
  j =  2                              :            45871
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  1.6e-3

Anderson-Darling statistic = A2       :    3.62
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:28.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:18.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:00.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.94e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:26.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:32.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:32.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.55
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.30
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.39
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.18
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:47.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.96
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.88
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.14
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.47
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17400.90
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.78
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   15.99
p-value of test                       :    0.9976


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.56
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.64
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.56
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.88
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.26
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.09
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.83
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.79
p-value of test                       :    0.9924


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  563.50
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.17
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.11
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.81
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.55
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.57
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.11
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.44
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.57
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.57
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.66
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.00
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.89
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.80
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.94
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.98
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.51
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.89
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.95
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:24.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.14
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:26.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.05e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 4.36e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 2.29e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.94
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.91
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.49
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.99
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:05.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10219.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9947.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:38.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4975.11
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4751.29
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.81
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.39
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11929.92
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.92
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000045523

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.64
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999993302

Normal statistic for number of bits   :  -0.053
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:02.86

 All tests were passed




Server wird beendet - Lösche Semaphor 110952460.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5406
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:54.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:40.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:04.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:04.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:54.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:58.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    3.69
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:12.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    2.83
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:43.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.25
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.71
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.16
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.32
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.70
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.92
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1563.52
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:02.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6862.81
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.49
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:06.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.09
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.66
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:32.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5118.66
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:57.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45903
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869903
  j =  1                              :        399908195
  j =  2                              :            45901
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869892
  j =  1                              :        399908217
  j =  2                              :            45890
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:28.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :  2.0e-3

Anderson-Darling statistic = A2       :    3.74
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:18.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:59.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:55.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:32.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.76e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.82e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:33.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:33.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.97
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.12
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.94
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.77
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:37.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.95
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.28
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.89
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17273.75
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.27
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.32
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.38
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.44
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.26
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.43
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.49
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.80
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.47
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.97
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.12
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.49
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.22
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.77
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.17
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.45
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.40
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.59
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.27
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.56
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.61
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.15
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  449.36
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4931.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.34
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.66
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:23.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.17
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.27
p-value of test                       :    0.99

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 6.81e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.38
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.92
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.65
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:06.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.54
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:03.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10105.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10261.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:40.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5075.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.77
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.19
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4256.92
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11688.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11949.90
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.36
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999849884

Normal statistic for number of bits   :   -1.19
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.44
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000219430

Normal statistic for number of bits   :    1.73
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.073
p-value of test                       :    0.53

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.93
p-value of test                       :    0.03

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:39.43

 All tests were passed




Server wird beendet - Lösche Semaphor 111902732.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5298
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:56.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:43.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:08.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:06.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:57.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:56.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.32
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:12.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:39.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.49
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.59
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.19
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.91
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.85
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.59
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.58
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  486.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:43.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.94
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:04.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7016.75
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.81
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:05.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.76
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.90
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5064.05
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:57.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45800
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869800
  j =  1                              :        399908401
  j =  2                              :            45798
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46046
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870046
  j =  1                              :        399907912
  j =  2                              :            46038
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:28.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:18.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 6.15e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.040
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:38.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.04
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.33
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.50
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.94
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.70
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17847.95
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.06
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.88
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.15
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.93
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.38
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   44.53
p-value of test                       :  9.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.17
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.80
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.66
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.85
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.07
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.33
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.77
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.11
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.11
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.52
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.63
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.44
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.48
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.45
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.58
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.58
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.55
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.13
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4874.55
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.71
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.46
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   0.079
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:21.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.94
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.01
p-value of test                       :    0.98

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.26e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.31
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.44
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.03
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:06.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.45
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10021.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9918.81
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:04:04.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5079.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.6e-3

Kolmogorov-Smirnov- statistic = D-    : 4.11e-3
p-value of test                       :    0.9957

Anderson-Darling statistic = A2       :    8.11
p-value of test                       :  1.1e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4509.01
p-value of test                       : 1 -  3.9e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:51.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.38
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.01
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11696.95
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11987.36
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:30.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.84
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999984074

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.10
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000003319

Normal statistic for number of bits   :   0.026
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:57.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 96  HammingIndep, L=30, r=27       1 -  3.9e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 112885772.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5355
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:56.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7108
p-value of test                       :    0.9931


-----------------------------------------------
CPU time used                    :  00:02:43.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4496
p-value of test                       :  8.2e-3


-----------------------------------------------
CPU time used                    :  00:02:00.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:09.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:07.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:00.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.58
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:12.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:43.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.26
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.79
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.58
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.56
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.43
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  179.89
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.40
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.48
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:05.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6884.22
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.17
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.45
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:07.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.09
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.44
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5184.62
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:58.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45900
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869900
  j =  1                              :        399908202
  j =  2                              :            45896
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45833
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869833
  j =  1                              :        399908339
  j =  2                              :            45823
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:28.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:18.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:02.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.50e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:41.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.19
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.16
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.47
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.62
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.13
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17434.93
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.21
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.33
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.07
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.52
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.45
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.58
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.54
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.50
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.34
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.65
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.58
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.04
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.91
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.11
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.57
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.94
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.18
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.30
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.84
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  256.37
p-value of test                       :  4.4e-3


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.43
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.09
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.62
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.10
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.38
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.53
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :  -0.086
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:22.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.24
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -2.19
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:22.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    2.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.22
p-value of test                       :    0.99

Sample variance                       :    2.33
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.75e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.75e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.14
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   41.00
p-value of test                       :  2.3e-3



-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.07
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.94
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:04.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.25
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:05.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.47
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.25
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:04:17.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.14
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:53.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.27
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:54.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4259.05
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11772.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:31.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11623.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:31.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.21
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999971201

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.42
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000027136

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.27

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:39.37

 All tests were passed




Server wird beendet - Lösche Semaphor 113967116.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5569
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:56.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4208
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:42.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:05.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:55.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:59.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    3.37
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     982
p-value of test                       :  3.7e-3

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    3.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9921

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:12.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:38.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.55
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.44
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.17
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.04
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.14
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  497.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.70
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6916.41
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.04
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.75
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:04.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.42
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.30
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:32.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4868.87
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:57.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45775
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869775
  j =  1                              :        399908451
  j =  2                              :            45773
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45994
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869994
  j =  1                              :        399908018
  j =  2                              :            45982
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:27.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:18.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:02.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:55.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :  1.1e-3

Anderson-Darling statistic = A2       :    6.94
p-value of test                       :  3.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:32.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.74e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.66e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:36.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.83
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.06
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.74
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.10
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.91
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.11
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.15
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.62
p-value of test                       :  1.5e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    5.83
p-value of test                       :  1.3e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   84.66
p-value of test                       :    0.9993    *****

-----------------------------------------------
CPU time used                    :  00:00:39.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17301.88
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.34
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.18
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.34
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.51
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.65
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.54
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.09
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.26
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.94
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.74
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.76
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.06
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.05
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.10
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.66
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.78
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.37
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.55
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.06
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.04
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.48
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.62
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.82
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.68
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.48
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.67
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.65
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.45
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.29
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.55
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.89
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    2.92
p-value of test                       :  1.8e-3



-----------------------------------------------
CPU time used                    :  00:02:23.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.89
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:23.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.29
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.11
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.19
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:04.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.28
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:03.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9833.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9892.02
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:41.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.66
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:49.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.03
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4421.03
p-value of test                       :  5.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.61
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11834.95
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11831.64
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.25
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999895820

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.93
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999968273

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:04.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 51  SampleProd, t = 16              3.8e-4
 72  Savir2                          0.9993 
 97  HammingIndep, L=300, r=0        5.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 114982924.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1210
p-value of test                       : 1 -  1.1e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334330
  j =  1                              :        599997580
  j =  2                              :             1210
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5340
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:56.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7473
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:43.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:05.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:05.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:00.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:14.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.96
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:42.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    5.83
p-value of test                       :    0.9968

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.40
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.51
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.63
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.70
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.02
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7126.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.92
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.83
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:04.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.36
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5076.23
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:56.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46139
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870139
  j =  1                              :        399907726
  j =  2                              :            46131
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45463
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869463
  j =  1                              :        399909075
  j =  2                              :            45461
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:26.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:17.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:59.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:33.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.79e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.75e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:34.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:34.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.09
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.01
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:47.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.89
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.42
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.00
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.98
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.17
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.65
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17573.63
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.61
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.37
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.74
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.70
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.09
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.37
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.61
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.22
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.91
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.99
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.19
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.20
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  566.58
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.14
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  105.40
p-value of test                       :  9.7e-3


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.90
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.11
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.30
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.14
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.50
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.18
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.34
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4900.82
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.75
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.14
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.80
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.68
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.53
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.91
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.24
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.61
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    1.60
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:25.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.87
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:25.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.12e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 8.15e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.99
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.90
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.14
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:06.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10172.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9833.41
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4774.93
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4782.18
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.81
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.81
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11758.48
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11593.03
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:30.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.12
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000060721

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.27
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000069031

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:15.13
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21          1 -  1.1e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 115998732.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5354
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:57.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:44.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4471
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:58.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:05.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:06.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:56.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7468
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:01.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.30
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.74
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:13.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:43.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.84
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.20
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.39
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.12
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.44
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  195.37
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.07
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:43.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1382.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:01.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6943.93
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.68
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:04.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.36
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  147.88
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5180.62
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:56.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869769
  j =  1                              :        399908468
  j =  2                              :            45757
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45839
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869839
  j =  1                              :        399908322
  j =  2                              :            45839
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:27.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:17.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:45.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.59e-3
p-value of test                       :    0.9938

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    4.53
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:34.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 7.54e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 8.56e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:35.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.35
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.51
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.31
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:47.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.41
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.97
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:39.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.84
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.51
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.78
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.57
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.57
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17313.36
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.75
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.89
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.26
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.59
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.00
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.09
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.11
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.49
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.76
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.50
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.05
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.59
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.59
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.14
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.40
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.23
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.77
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.43
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.89
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.70
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.07
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5105.82
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.39
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.65
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.67
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.15
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.06
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.11
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.64
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.20
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:22.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.46
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:23.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.04
p-value of test                       :    0.98

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.60e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.40
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.71
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:05.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.98
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:07.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.02
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10200.04
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:38.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4782.28
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:49.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.28
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.36
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4329.18
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11832.91
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11489.14
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.07
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000120913

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.61
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999983723

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:26.14

 All tests were passed




Server wird beendet - Lösche Semaphor 117014540.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5344
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:57.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4202
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4205
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:58.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:06.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:55.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:00.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:52.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    3.82
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     334
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:14.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:44.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.26
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.09
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.91
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.55
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.70
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.83
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.25
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1518.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:01.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7050.33
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.87
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:04.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.54
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.88
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:32.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4923.72
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:56.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45754
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869754
  j =  1                              :        399908498
  j =  2                              :            45742
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46481
p-value of test                       :  2.5e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870481
  j =  1                              :        399907044
  j =  2                              :            46469
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:26.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:18.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:33.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.82e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.85e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.45e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.044
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:33.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:34.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.71
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.94
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.95
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.44
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.52
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:38.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.82
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.13
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17266.85
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.01
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.75
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.57
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.91
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.79
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.42
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.28
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.53
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.59
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.43
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.34
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.89
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.93
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.21
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.67
p-value of test                       :    0.9951


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.80
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  100.54
p-value of test                       :    0.9901


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.77
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.38
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4874.17
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.47
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.00
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.14
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.71
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.17
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.10
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.82
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.96
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:23.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.43
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -1.10
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:23.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.70e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.67e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.11
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.36
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.83
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:04.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  1.9e-3

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10177.76
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:44.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5035.40
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.34
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.45
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.93
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11728.05
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11761.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:29.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.99
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000178489

Normal statistic for number of bits   :    1.41
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.35
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000144112

Normal statistic for number of bits   :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:30.62

 All tests were passed




Server wird beendet - Lösche Semaphor 118030348.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:56.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:42.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4224
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:58.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:06.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:07.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7108
p-value of test                       :    0.9931


-----------------------------------------------
CPU time used                    :  00:03:55.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:00.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.94
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.32
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:14.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.96
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.58
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.50
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.40
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.80
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.10
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.29
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.18
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:52.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1356.25
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:09.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7167.73
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:55.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.69
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.09
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:03.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.33
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.92
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4949.51
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:56.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45767
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869767
  j =  1                              :        399908468
  j =  2                              :            45763
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45540
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869540
  j =  1                              :        399908924
  j =  2                              :            45532
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:26.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:17.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:44.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:00.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 9.39e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.46e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.83e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 2.67e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:27.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.041
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:34.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:48.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.41
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.34
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.37
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:47.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:38.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.96
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.031
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17241.47
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.68
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.80
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.20
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.04
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.46
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.10
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.89
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.83
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.50
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.41
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.88
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.73
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.10
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.54
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.53
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.14
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.69
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.13
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.46
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.64
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.38
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  453.13
p-value of test                       :  8.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5161.00
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.70
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.10
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.89
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.08
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.64
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.11
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.26
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.80
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:22.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.26
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.79
p-value of test                       :    0.04

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :  7.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.09
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.06
p-value of test                       :    0.9978

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:04.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
p-value of test                       :    0.9928

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  249.65
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:02:06.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9790.80
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9846.14
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:40.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.13
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5035.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.37
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.33
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11695.38
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.48
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000074884

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.92
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  7999967346

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:04.32

 All tests were passed




Server wird beendet - Lösche Semaphor 119046156.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5294
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:57.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:42.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7114
p-value of test                       :    0.9916


-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:06.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:56.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:00.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.04
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:14.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:44.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.66
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.04
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.06
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.07
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.45
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.20
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  383.95
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:43.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.83
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:02.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6989.72
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.49
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.40
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:04.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.94
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.20
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:32.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4879.76
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:11.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:55.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45502
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869502
  j =  1                              :        399909002
  j =  2                              :            45490
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46073
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870073
  j =  1                              :        399907854
  j =  2                              :            46073
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:26.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:18.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:00.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:54.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:34.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.92e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.39e-6
p-value of test                       :    0.9965

Kolmogorov-Smirnov- statistic = D-    : 3.87e-4
p-value of test                       :  2.5e-3

Anderson-Darling statistic = A2       :    5.21
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:34.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.54
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.68
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.66
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.57
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.61
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.16
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.56
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17252.83
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.34
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.05
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.51
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.04
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.79
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.45
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.68
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.44
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.23
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.69
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.31
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.32
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.95
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.77
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.10
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.23
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.17
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.07
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.11
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.96
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.99
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.92
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.21
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.08
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.87
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.23
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.01
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4825.36
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.16
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.17
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.89
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:22.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.28
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :   -1.79
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 5.75e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.60e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 8.95e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.31
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.28
p-value of test                       :    0.9957

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.14
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:05.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.58
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:06.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 9.24e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9722.86
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.53
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:42.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.10
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4765.98
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4245.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.36
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.82
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.28
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.11
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999980501

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.91
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000006859

Normal statistic for number of bits   :   0.054
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.98
p-value of test                       :    0.02

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:16.77

 All tests were passed




Server wird beendet - Lösche Semaphor 120061964.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5461
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:58.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:43.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:06.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7525
p-value of test                       :  8.2e-3


-----------------------------------------------
CPU time used                    :  00:03:06.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:56.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:00.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.42
p-value of test                       :  5.5e-3

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    2.35
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    3.63
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:13.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:43.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.66
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.45
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  496.84
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:43.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.61
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6905.98
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.59
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.87
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.85
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:33.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4998.06
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:52.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46259
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870259
  j =  1                              :        399907485
  j =  2                              :            46253
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45871
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869871
  j =  1                              :        399908263
  j =  2                              :            45861
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:24.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:16.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:44.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:59.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:54.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 5.94e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.73e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.036
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:33.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.68
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.72
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.39
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:37.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.38
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.85
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.01
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:39.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17535.82
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.10
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.85
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.55
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.54
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.33
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.04
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.25
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.05
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.51
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.56
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.53
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.64
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.26
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.73
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.03
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.80
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.20
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.61
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.04
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.25
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.15
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.62
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.87
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.07
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.40
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.07
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.82
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.47
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.92
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.81
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:23.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.82
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.96e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.48e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.32
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.04
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:04.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.07
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:05.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9934.42
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10064.91
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:42.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4767.91
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:49.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.98
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:51.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4248.67
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11703.24
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11580.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.25
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999958439

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.61
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999864317

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.035
p-value of test                       :    0.49

Sample variance                       :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:41.35

 All tests were passed




Server wird beendet - Lösche Semaphor 121077772.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5491
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:41.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:36.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:33.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:54.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:01.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:01.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:53.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:59.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.53
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    2.72
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.77
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:11.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.12
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:36.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.95
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.66
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.56
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.99
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.89
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.65
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.28
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1534.51
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:59.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6978.51
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.73
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:03.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.98
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.76
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:35.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4948.95
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:04.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45985
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869985
  j =  1                              :        399908035
  j =  2                              :            45975
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45391
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869391
  j =  1                              :        399909219
  j =  2                              :            45389
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:29.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:59.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 2.95e-3
p-value of test                       :    0.9969

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:34.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.71e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:34.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.023
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:39.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.34
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:47.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.19
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.46
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.25
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.33
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.55
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.95
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.18
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17377.77
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.16
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.09
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.68
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.39
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.30
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.67
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.34
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.37
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.29
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.27
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.94
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  177.26
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.23
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:47.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.91
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.35
p-value of test                       :    0.9915


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.16
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.69
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.63
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:46.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.62
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.91
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.87
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.43
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.57
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.23
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.23
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5098.03
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.26
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.59
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.81
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:23.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.47
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -1.15
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:17.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.94e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.89e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 4.20e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.16
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.74
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.10
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:08.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9860.39
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9846.13
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.085
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:45.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4708.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.99
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11679.07
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.77
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999902576

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.23
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999961277

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    2.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:26.23

 All tests were passed




Server wird beendet - Lösche Semaphor 102006797.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5299
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:44.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:34.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:54.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4473
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:55.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:00.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7469
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:01.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7460
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:53.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:58.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    2.73
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     969
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:46.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:10.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:37.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.23
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.32
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.96
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.54
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6995.24
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:41.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.87
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:04.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.39
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:47.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.09
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5014.37
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:03.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45721
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869721
  j =  1                              :        399908566
  j =  2                              :            45705
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46093
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870093
  j =  1                              :        399907816
  j =  2                              :            46089
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:29.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 2.85e-4
p-value of test                       :    0.9997    *****

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:19.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:45.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:00.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:53.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.11e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 4.26e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:40.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.89
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:47.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.42
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.48
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.71
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:47.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.43
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.61
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.17
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.71
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.62
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17489.98
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.48
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.55
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.85
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.15
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.79
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:39.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.33
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.45
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.22
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.32
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.67
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.93
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.83
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  566.16
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.34
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.34
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.97
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.87
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.73
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.26
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.10
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.10
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.77
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.90
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.08
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.22
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.19
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.17
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4831.87
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.75
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.39
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.08
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:21.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.38
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -1.55
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:18.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.86
p-value of test                       :    0.03

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -2.09
p-value of test                       :    0.98

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.63e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.55
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.81
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.09
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:08.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.12
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:08.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10155.63
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10204.41
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.077
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:04:08.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.75
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.80
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3902.28
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11640.11
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11494.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.55
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000010321

Normal statistic for number of bits   :   0.082
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.25
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000030664

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:28.55

 All tests were passed




Server wird beendet - Lösche Semaphor 102760461.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5484
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:47.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:37.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:36.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:55.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:01.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:01.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:53.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:58.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.83
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:46.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.29
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.92
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.18
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:02:09.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:42.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.30
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.12
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.78
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.30
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.09
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.91
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.93
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.49
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.78
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7207.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:41.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.83
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:04.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.12
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:47.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.30
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.59
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:02.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45494
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869494
  j =  1                              :        399909018
  j =  2                              :            45482
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45697
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869697
  j =  1                              :        399908612
  j =  2                              :            45685
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:28.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:20.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:54.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:32.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 2.74e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:35.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.91
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.57
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:00:47.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.56
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:47.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.89
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.82
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:40.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.82
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.29
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.29
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.42
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17315.12
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.97
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.19
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.73
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.97
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.95
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.43
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.23
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.73
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.87
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.62
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.13
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.02
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.17
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.05
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.47
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.57
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.92
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.35
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.47
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.00
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.89
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5163.55
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.29
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.97
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.30
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.31
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.30
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.76
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.43
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:34.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.74
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:19.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.01
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 4.26e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 6.62e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.19
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.91
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.13
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:08.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:08.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.3e-3

Anderson-Darling statistic = A2       :    5.36
p-value of test                       :  2.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10448.47
p-value of test                       :  8.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.65
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:54.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.75
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.79
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.33
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4002.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11548.52
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11907.59
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.49
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000046030

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.50
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999898544

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:34.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 90  HammingWeight2, r = 0           8.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 103907341.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5359
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:50.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:59.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:08.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:09.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:07.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:11.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:02.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.92
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    3.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:16.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.84
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    2.82
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:45.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.55
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.08
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.73
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.48
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.28
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:59.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1497.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:10.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7110.34
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.79
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:08.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.62
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.53
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4943.19
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:14.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45953
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869953
  j =  1                              :        399908096
  j =  2                              :            45949
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45635
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869635
  j =  1                              :        399908733
  j =  2                              :            45629
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:36.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:21.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.25e-3
p-value of test                       :    0.9936

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 4.46e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.067
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:25.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.016
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.43
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.00
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.49
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.40
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.59
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:51.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.50
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.96
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17347.94
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.61
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.86
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.51
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.18
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.18
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.02
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.75
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.70
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.65
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.53
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.78
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.29
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.81
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.85
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.49
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.65
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.03
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.60
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.05
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.90
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.82
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.49
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.90
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.59
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.14
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.21
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.45
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.50
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.33
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.12
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:27.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.07
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:26.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.40e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.86e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 8.57e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.43
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.73
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:10.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10115.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10122.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:05:22.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.77
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:51.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.76
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.62
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11732.80
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:32.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.25
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.74
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000038485

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.49
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999968816

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:14:52.06

 All tests were passed




Server wird beendet - Lösche Semaphor 104955917.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  3.9e-3


-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:50.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:37.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:04.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:57.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:02.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.68
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:13.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:41.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.13
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.18
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.27
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.61
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.99
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.89
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.10
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.87
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  392.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.60
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7163.03
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.17
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:03.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.40
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.42
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4953.95
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:03.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46142
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870142
  j =  1                              :        399907721
  j =  2                              :            46132
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45794
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869794
  j =  1                              :        399908417
  j =  2                              :            45784
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:27.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:18.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:54.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.11e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.53
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.53
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.81
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.85
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.50
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.74
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.48
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:37.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.85
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17519.37
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.40
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.05
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.24
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.50
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.85
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.73
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.40
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   46.10
p-value of test                       :  6.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.27
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.29
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.44
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.36
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.57
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.71
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.28
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.02
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.21
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.06
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.54
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.44
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.70
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.01
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.65
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.75
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.61
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.91
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.71
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4797.27
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.68
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.65
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.29
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    1.30
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:23.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.13
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -1.19
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:23.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.96
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.18
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.08
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:06.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.09
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:07.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.31
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10120.57
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:44.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.58e-3
p-value of test                       :    0.9952

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5102.29
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.52
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.34
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11766.99
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.38
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.45
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999911483

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.86
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999865193

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:33.73

 All tests were passed




Server wird beendet - Lösche Semaphor 106364941.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5287
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:50.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:39.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:36.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4239
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:03.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:04.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:55.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:01.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.23
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:13.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    2.11
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    3.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:40.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.80
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.69
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.13
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.39
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.74
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:42.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.49
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7011.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.27
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.78
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:02.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.15
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.38
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:33.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5116.39
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:58.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46179
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870179
  j =  1                              :        399907643
  j =  2                              :            46177
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45996
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869996
  j =  1                              :        399908010
  j =  2                              :            45992
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:26.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:17.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:54.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.70e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.54e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.063
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.84
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.54
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.50
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.29
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.14
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.11
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:38.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.3e-3

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.16
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.87
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.00
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17532.05
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.74
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.24
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.74
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.64
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.32
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.87
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.33
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.16
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.80
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.44
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.35
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.31
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.97
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.07
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.90
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.20
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   92.76
p-value of test                       :    0.9983


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.54
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.93
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.65
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5151.50
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  318.10
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.75
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.12
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.92
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.86
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.00
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.31
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:25.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.75
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:24.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.18
p-value of test                       :    0.01

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.17

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.53e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.87e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 3.77e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.36
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.13
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.64
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.62
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:08.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10226.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9867.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.074
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:40.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.59
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.46
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4251.53
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.30
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.42
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.73
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.52
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999979172

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.83
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000139672

Normal statistic for number of bits   :    1.10
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:58.70

 All tests were passed




Server wird beendet - Lösche Semaphor 107315213.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1470
p-value of test                       :  2.4e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334590
  j =  1                              :        599997060
  j =  2                              :             1470
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5339
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:49.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:36.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:05.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:59.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:01.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.99
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    2.10
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:13.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.95
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.50
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.02
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.18
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.72
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.82
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  500.95
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.11
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:04.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7035.04
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:50.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.15
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:10.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.28
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.45
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4914.87
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:04.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45935
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869935
  j =  1                              :        399908134
  j =  2                              :            45927
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46164
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870164
  j =  1                              :        399907675
  j =  2                              :            46158
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9948

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:28.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:18.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:59.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 5.62e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.29e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.45
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.19
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.78
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.29
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.06
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17556.78
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.35
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.72
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.66
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.23
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.08
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.42
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.25
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.46
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.58
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.32
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.16
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.98
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.18
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.84
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.74
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.42
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.90
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.10
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.77
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.62
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.87
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4879.55
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  323.85
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.43
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.55
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.35
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.81
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.37
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.71
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.00
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -1.00
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.72
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:24.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.24e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.49e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.29
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.32
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.96
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:07.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.42e-3
p-value of test                       :    0.9943

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  250.41
p-value of test                       :  8.9e-3

-----------------------------------------------
CPU time used                    :  00:02:06.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10283.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:04:17.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4812.60
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:53.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5032.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3850.73
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11977.39
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.02
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.38
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000145195

Normal statistic for number of bits   :    1.15
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.53
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000040591

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:32.48

 All tests were passed




Server wird beendet - Lösche Semaphor 108363789.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5493
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:51.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:03.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:04.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:54.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:44.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.79
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.19
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.25
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.76
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.51
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.36
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.71
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.63
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.02
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:43.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6843.55
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.55
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.05
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:02.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.62
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.08
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4972.70
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:57.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45844
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869844
  j =  1                              :        399908316
  j =  2                              :            45836
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45941
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869941
  j =  1                              :        399908120
  j =  2                              :            45937
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:25.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:16.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :  1.1e-3

Anderson-Darling statistic = A2       :    4.68
p-value of test                       :  4.2e-3


-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:54.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:35.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 8.22e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-5
p-value of test                       :    0.9917

Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:35.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.72
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:47.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.04
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.82
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.18
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.75
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.45
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.78
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :  9.8e-4    *****

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.21
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17317.18
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.13
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.77
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.26
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.51
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.89
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.86
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.91
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.23
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.34
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.74
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.70
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.78
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.94
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.70
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.98
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.31
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.31
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.25
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.26
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.12
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.03
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.57
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.18
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.65
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.65
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.99
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4812.55
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.91
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.02
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.79
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:23.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.71
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.38e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 9.81e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.57e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.95
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.96
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.74
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:06.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:07.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10055.26
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
p-value of test                       :    0.9998    *****

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9699.49
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.014
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:41.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.72
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :  7.7e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    6.90
p-value of test                       :  4.1e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4637.86
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:01:50.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4051.14
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11678.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11506.40
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.06
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000008152

Normal statistic for number of bits   :   0.064
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.76
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999953792

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.17
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:20.13

 All tests were passed




Server wird beendet - Lösche Semaphor 109445133.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1240
p-value of test                       :    0.9997    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334360
  j =  1                              :        599997520
  j =  2                              :             1240
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:52.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7138
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:38.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:58.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:01.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.69
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    2.60
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     658
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:13.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:40.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.56
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.21
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   86.86
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.88
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:29.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.52
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.84
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.22
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.34
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.49
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:03.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7149.16
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.30
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.08
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:31.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.02
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.44
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5105.42
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:02.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45953
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869953
  j =  1                              :        399908095
  j =  2                              :            45951
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45539
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869539
  j =  1                              :        399908926
  j =  2                              :            45531
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:28.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:18.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:02.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.58e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.25e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 9.75e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.04
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.54
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.49
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   54.02
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.88
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.94
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17419.46
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.30
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.12
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.05
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.21
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.42
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.25
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.49
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.77
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.08
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.75
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.44
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.27
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.47
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.38
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.86
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.38
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.16
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.72
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.29
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  447.70
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4895.53
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.08
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.61
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.15
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.54
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5225.33
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.49
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.47
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.26
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -1.90
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:23.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.19
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:24.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9973

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   29.54
p-value of test                       :  2.5e-4    *****

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.86
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.68
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:05.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.48
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9868.12
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9945.33
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:04:20.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    4.04
p-value of test                       :  8.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5169.88
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:01:54.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4933.48
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:54.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.07
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4004.09
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11817.35
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11594.29
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.08
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000081061

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.62
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000109270

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:56.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9997 
 86  LongestHeadRun, r = 0           2.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 110362637.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5312
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:53.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:04.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7132
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7490
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:56.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:04:02.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.22
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     950
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    2.10
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.42
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9945

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:14.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.56
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.38
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.57
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.91
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.81
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.24
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6915.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:41.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.48
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.35
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:03.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.31
p-value of test                       :    0.9974


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.08
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5051.42
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:57.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46014
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870014
  j =  1                              :        399907980
  j =  2                              :            45998
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45563
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869563
  j =  1                              :        399908876
  j =  2                              :            45559
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:27.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:18.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:01.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :  2.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:33.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.79e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 3.26e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:43.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.65
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.63
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.82
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.13
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.14
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.62
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.71
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.47
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17317.98
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.23
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.17
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.40
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.72
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.54
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.02
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.16
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.19
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.38
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.56
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.10
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.80
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.08
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.59
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.27
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.49
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.76
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.30
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.33
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.89
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.69
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.67
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5225.93
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.44
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.60
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.44
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.20
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.88
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.28
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :   -2.55
p-value of test                       :    0.9946



-----------------------------------------------
CPU time used                    :  00:02:23.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.61
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:24.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.21e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.91e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 6.94e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.89
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.89
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.51
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.72
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:05.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.34
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9866.63
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:41.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5074.64
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.54
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4232.02
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3985.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11867.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11675.36
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.15
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999987368

Normal statistic for number of bits   :  -0.100
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.03
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000171973

Normal statistic for number of bits   :    1.36
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:54.87

 All tests were passed




Server wird beendet - Lösche Semaphor 111443981.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:51.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4435
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:40.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:04.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:55.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:01.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    3.28
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:13.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.07
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:41.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.13
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.20
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.00
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.34
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.77
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.57
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.65
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:02.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6952.36
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.14
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:02.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.35
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.49
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:32.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5001.93
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:58.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45923
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869923
  j =  1                              :        399908157
  j =  2                              :            45917
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45267
p-value of test                       :    0.9979


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869267
  j =  1                              :        399909474
  j =  2                              :            45251
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:27.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:18.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:59.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:55.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.42e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.070
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:38.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:38.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.28
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.36
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.73
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   11.38
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:01:42.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.40
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17386.56
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.04
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.57
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.60
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.44
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.35
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.27
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.84
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.29
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.57
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.76
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.70
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.97
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.43
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.90
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.90
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.53
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.46
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.97
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.99
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.27
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.00
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.46
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4885.22
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.73
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.78
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.52
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.87
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.41
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.00
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.87
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.79
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :  -0.028
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:24.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.11e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 7.81e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.45e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 6.23e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.12
p-value of test                       :    0.9998    *****

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.73
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.52
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:06.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:06.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9836.85
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10073.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:40.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5028.93
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.05
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.50
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11623.72
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11613.36
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.66
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000001312

Normal statistic for number of bits   :   0.010
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.45
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999921071

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :  -0.079
p-value of test                       :    0.53

Sample variance                       :    2.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:00.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 85  Fourier3, r = 27                0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 112394253.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  9.5e-3


-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5329
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:54.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:52.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4167
p-value of test                       :    0.9951


-----------------------------------------------
CPU time used                    :  00:02:02.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:11.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:31.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:29.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:11.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:46.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:13.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:41.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.86
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.83
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.47
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.98
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.13
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.26
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.71
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:02.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7150.12
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.62
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.23
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:02.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.29
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.47
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:33.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4979.38
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:00.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908185
  j =  2                              :            45903
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46043
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870043
  j =  1                              :        399907917
  j =  2                              :            46037
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:25.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:32.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:55.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.33e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 8.39e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:35.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.13
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.02
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.98
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.85
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:41.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.66
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.11
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.82
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17560.09
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.59
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.16
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.11
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   35.58
p-value of test                       :  5.2e-3


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.91
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.26
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.37
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.96
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.53
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.31
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.67
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.38
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.66
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.05
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.40
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.79
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.10
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.39
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.63
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5295.37
p-value of test                       :  1.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.98
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.46
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.18
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.47
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.44
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.82
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.97
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.65
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -1.63
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.68e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 6.45e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.64e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 8.61e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.74
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.57
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:07.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:07.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10096.21
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9911.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:37.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.18
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3961.62
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.99
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11705.12
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11750.76
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.30
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999976352

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.25
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000060013

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:08.43

 All tests were passed




Server wird beendet - Lösche Semaphor 113344525.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5269
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:52.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:39.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4448
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:03.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:03.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:54.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:59.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    2.28
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     967
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:13.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:42.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.46
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.95
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.55
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.56
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.68
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.20
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.82
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.14
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.98
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.11
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.61
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6839.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:42.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.28
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.20
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:32.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5070.74
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9984


-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46232
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870232
  j =  1                              :        399907538
  j =  2                              :            46228
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45857
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869857
  j =  1                              :        399908290
  j =  2                              :            45849
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:27.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  8.8e-3

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:17.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:33.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:34.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.72
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.49
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:47.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.94
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.61
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.69
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.55
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17444.59
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.18
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.47
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.48
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.75
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.68
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.45
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.04
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.95
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.57
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.82
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.89
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.75
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.31
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.91
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.54
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.52
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.82
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.11
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.86
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5095.93
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.73
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.27
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.43
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.61
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.73
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.43
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.55
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:24.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.21
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9913

Tests on the sum of all N observations
Standardized normal statistic         :  -0.060
p-value of test                       :    0.52

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 5.92e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.02e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.62
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.30
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.38
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.43
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10113.21
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10024.12
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.031
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:41.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.38
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4849.20
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.84
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.17
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11707.14
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.41
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.20
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000010852

Normal statistic for number of bits   :   0.086
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.93
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999974420

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.94
p-value of test                       :    0.97

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.93

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:23.22

 All tests were passed




Server wird beendet - Lösche Semaphor 114294797.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5309
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:39.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4484
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:57.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:04.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:03.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:53.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:58.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:45.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     261
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:13.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:42.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.24
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.56
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.23
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.74
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  485.11
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:43.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.22
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:02.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7041.57
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:05.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.49
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:46.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.43
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4905.62
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:58.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46157
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870157
  j =  1                              :        399907689
  j =  2                              :            46151
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46280
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870280
  j =  1                              :        399907447
  j =  2                              :            46266
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:26.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:18.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:46.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9906


-----------------------------------------------
CPU time used                    :  00:01:59.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:35.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.68e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.90e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  119.57
p-value of test                       :  8.3e-5    *****

-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.53
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.55
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.33
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.52
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.15
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.52
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.13
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    3.35
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17061.16
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.93
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.39
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.22
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.59
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.26
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.16
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.63
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.23
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.99
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.78
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.51
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.10
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.41
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.74
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.95
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.21
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.99
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.77
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:43.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.84
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.52
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.19
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.54
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.86
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.74
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.97
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.25
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.20
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.36
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:22.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.70
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -1.23
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:22.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   0.087
p-value of test                       :    0.47

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.92e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 9.70e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 7.33e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.28
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.01
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.64
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:05.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:07.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.92
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9781.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:40.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.75
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4751.27
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.46
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11578.26
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11620.04
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.59
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000078064

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.84
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999938840

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.09
p-value of test                       :    0.02

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:36.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 59  WeightDistrib, r = 0            8.3e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 115146765.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:17.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1478
p-value of test                       :  1.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334598
  j =  1                              :        599997044
  j =  2                              :             1478
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5342
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:56.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7159
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:40.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4460
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:05.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:54.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:59.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9931

Test on the Nm values of W_{n,i}(mNP1):    3.88
p-value of test                       :  9.9e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     967
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:11.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.10
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.39
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.42
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.52
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.51
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.07
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7009.41
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:42.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.02
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:04.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.81
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.95
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:33.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.34
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:58.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46056
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870056
  j =  1                              :        399907891
  j =  2                              :            46050
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45883
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869883
  j =  1                              :        399908235
  j =  2                              :            45881
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:27.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:59.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:55.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:32.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.94e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.76e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:34.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.74
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.57
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.00
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.11
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.65
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.20
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.32
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:39.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17534.17
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.36
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.32
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.84
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.52
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.79
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.70
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.97
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.17
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.66
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.94
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.04
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.22
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.27
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.21
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.48
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.45
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.87
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  100.61
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.38
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.47
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.58
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.14
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.99
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.55
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.72
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.90
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.15
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.50
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:34.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.80
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.92
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -1.58
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:20.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.51e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.03e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 9.47e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.90
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.81
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.37
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:05.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.47
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:05.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.37
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10063.67
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:40.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5006.73
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4765.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:51.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4228.09
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.85
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.63
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11718.27
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.49
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000014722

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.15
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000089674

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:28.89

 All tests were passed




Server wird beendet - Lösche Semaphor 116195341.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:51.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5497
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:55.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:41.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:06.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:04.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:54.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:59.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.45
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    2.16
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     845
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    2.70
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:13.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.93
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:44.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.31
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.44
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.87
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.94
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.80
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.08
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.35
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.33
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:44.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1483.66
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7301.76
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.21
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.58
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:03.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.39
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.54
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:33.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4935.97
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:02.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46017
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870017
  j =  1                              :        399907967
  j =  2                              :            46015
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45241
p-value of test                       :    0.9986


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869241
  j =  1                              :        399909518
  j =  2                              :            45241
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:27.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:18.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:58.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:32.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 3.27e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 8.02e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.045
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.63
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:48.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.53
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:43.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.32
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.87
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.87
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17290.61
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.04
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.32
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.23
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.08
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.66
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.91
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.34
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.48
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.27
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.41
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.05
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.41
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.46
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.93
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.45
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.46
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.12
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  107.53
p-value of test                       :  6.6e-3


-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.48
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.05
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.52
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.45
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  156.51
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.01
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.11
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.96
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.77
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.24
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.41
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -1.98
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.85
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    1.28
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    5.10
p-value of test                       :  2.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    3.86
p-value of test                       :  6.7e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.85e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.41
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.93
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.08
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:04.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.82
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:05.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9786.16
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10170.43
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:42.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4729.90
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:50.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11947.61
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11791.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.18
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999860978

Normal statistic for number of bits   :   -1.10
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.98
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000122458

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.01
p-value of test                       :    0.02

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.50
p-value of test                       :    0.93

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:42.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 27  SimpPoker, r = 27               0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 117243917.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5384
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:56.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:42.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:06.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:06.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7158
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:01.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    2.96
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     843
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:13.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:41.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.54
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.65
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.68
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.68
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.13
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.12
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.72
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.37
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:44.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.19
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7076.81
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:43.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.93
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:04.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.73
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.51
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:33.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4936.22
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:02.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45838
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869838
  j =  1                              :        399908329
  j =  2                              :            45828
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46397
p-value of test                       :  8.0e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870397
  j =  1                              :        399907210
  j =  2                              :            46389
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:18.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:44.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:59.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:33.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.88e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.94e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.60e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:37.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.73
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:48.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.77
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.10
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.24
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.69
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.80
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.69
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.68
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.27
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.27
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17608.64
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.94
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.12
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.19
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.32
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.11
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.53
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.24
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.97
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.54
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.08
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.18
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.63
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.82
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.58
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.18
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.06
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.28
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.06
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.29
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.01
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.50
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.65
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.74
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.46
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.83
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.84
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5088.89
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.26
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.71
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.90
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:24.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.95
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    1.37
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:23.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.90e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 3.89e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.28
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.63
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.84
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:05.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.5e-3

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.36
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:07.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10113.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9904.41
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.36
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:50.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.73
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4292.56
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11900.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11814.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.31
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999970100

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.38
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999951146

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:47.60

 All tests were passed




Server wird beendet - Lösche Semaphor 118194189.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1482
p-value of test                       :  8.6e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334602
  j =  1                              :        599997036
  j =  2                              :             1482
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5482
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:56.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:05.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:55.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:00.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    2.82
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    2.86
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:13.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:40.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.37
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.11
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.93
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.02
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.86
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.64
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1345.63
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6968.92
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.44
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:05.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.97
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.94
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5105.67
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:02.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45916
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869916
  j =  1                              :        399908173
  j =  2                              :            45906
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45952
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869952
  j =  1                              :        399908101
  j =  2                              :            45942
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:27.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:19.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:01.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.52e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.98e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.58e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.93e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:38.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.18
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:48.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.72
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.07
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:48.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.78
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.37
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:40.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.60
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.97
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:30.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.23
p-value of test                       :  7.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   88.59
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17670.43
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.05
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.43
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.37
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.77
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.34
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.43
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.40
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.00
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.68
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.05
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.22
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.15
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.00
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.63
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.39
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.48
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.16
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.80
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.65
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.22
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.45
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.68
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.50
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.75
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.00
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4841.13
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.82
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.38
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.05
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:23.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.85
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    0.66
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.20e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.75
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.72
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.28
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:05.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9824.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10131.74
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:41.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5012.00
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5029.22
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.11
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11945.98
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12073.17
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.61
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999994907

Normal statistic for number of bits   :  -0.040
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.12
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000012886

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.085
p-value of test                       :    0.47

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:37.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           8.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 119209997.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5415
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:58.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:41.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:58.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:05.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:55.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:00.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    2.57
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     548
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:12.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:39.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.55
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.06
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.76
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.11
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.86
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1382.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:02.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7217.00
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.05
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.12
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.84
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.60
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:33.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4935.61
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:58.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46153
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870153
  j =  1                              :        399907697
  j =  2                              :            46147
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46064
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870064
  j =  1                              :        399907874
  j =  2                              :            46060
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:27.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:19.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 4.87e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:39.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:47.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.97
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.93
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.57
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:41.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.36
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.71
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.07
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.48
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.20
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17315.67
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.01
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.95
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.28
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.99
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.28
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.99
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.35
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.90
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.69
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.71
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.13
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.55
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.17
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.44
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.27
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.10
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.99
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.50
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.32
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.60
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.03
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.46
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.11
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.84
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4896.79
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.40
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.29
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.30
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:23.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.97
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    2.40
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.66e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 8.15e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.98
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.66
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:04.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.58
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:05.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.54
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.31
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:40.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
p-value of test                       :    0.9902

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4677.15
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:48.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.93
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:50.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.87
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.66
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.22
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11786.77
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.15
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000094399

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.44
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000153583

Normal statistic for number of bits   :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.14
p-value of test                       :    0.02

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :  4.9e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.74
p-value of test                       :  4.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.54
p-value of test                       :    0.9945

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.52
p-value of test                       :    0.9941

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:24.98

 All tests were passed




Server wird beendet - Lösche Semaphor 120193037.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:40.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1247
p-value of test                       :    0.9993    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334367
  j =  1                              :        599997506
  j =  2                              :             1247
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5462
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:58.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:07.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:07.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:57.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:59.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.55
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    2.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9931


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:14.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:43.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.20
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.08
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.69
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.34
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.53
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.53
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.15
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.48
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:04.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6908.98
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:42.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.08
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.2e-3

Anderson-Darling statistic = A2       :    3.79
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.30
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.21
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:35.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5182.96
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:00.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45853
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869853
  j =  1                              :        399908301
  j =  2                              :            45839
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46056
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870056
  j =  1                              :        399907891
  j =  2                              :            46050
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:29.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:17.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:59.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.90e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.93
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:41.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.77
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.04
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.26
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.74
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.63
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.20
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.84
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.75
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.31
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.01
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17078.14
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.46
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.71
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.63
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.20
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.74
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.37
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.25
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.79
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.66
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.62
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.60
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.28
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.02
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.23
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.63
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.88
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.03
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.43
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.51
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.74
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.44
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  152.67
p-value of test                       :    0.9946


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.33
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.83
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.59
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.37
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.64
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.00
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :    1.64
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:24.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.72
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :  -0.100
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:25.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.23

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.51e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 9.04e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 9.33e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.35
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.51
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:02.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:02.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.20
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.21
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:33.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.00
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4781.63
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4018.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.91
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11627.56
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12055.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.05
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999993716

Normal statistic for number of bits   :  -0.050
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.65
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999981566

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:23.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 121176077.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1468
p-value of test                       :  2.8e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334588
  j =  1                              :        599997064
  j =  2                              :             1468
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5274
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:41.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:36.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:34.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:54.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:01.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:00.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:52.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:58.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    3.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.87
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:12.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:35.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.19
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.47
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.40
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.90
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.81
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  272.61
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.09
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:53.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.39
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:01.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7154.52
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.66
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:02.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.77
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.18
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:35.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4998.52
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:15.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46003
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870003
  j =  1                              :        399907997
  j =  2                              :            45997
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45621
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869621
  j =  1                              :        399908763
  j =  2                              :            45611
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:29.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:19.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:45.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:59.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:53.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:34.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.46e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.62e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.050
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:35.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.29
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.33
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.49
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.72
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.66
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.10
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.11
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17361.67
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.04
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.38
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.75
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.37
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.26
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.85
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.38
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.08
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.57
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.34
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:40.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.00
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.14
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   97.58
p-value of test                       :    0.9947


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.95
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.83
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.46
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  575.12
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.04
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.15
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.50
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.91
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.69
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.33
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.78
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.36
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5133.24
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.55
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.78
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.07
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:17.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.54
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:17.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.62e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.79e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.04
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.62
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:07.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:08.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10192.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9880.43
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.042
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.077
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:43.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.04
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:50.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.77
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11460.61
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11738.20
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.76
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999912533

Normal statistic for number of bits   :   -0.69
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.62
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000019105

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.069
p-value of test                       :    0.47

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:59.27

 All tests were passed




Server wird beendet - Lösche Semaphor 102039566.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5462
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:44.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4446
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4469
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:00.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:02.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:54.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7521
p-value of test                       :  9.3e-3


-----------------------------------------------
CPU time used                    :  00:03:58.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:04.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:31.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.20
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.04
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.19
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.43
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.92
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.58
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:45.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.42
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7143.06
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.52
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:04.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.17
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.99
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4903.47
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:25.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46078
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870078
  j =  1                              :        399907847
  j =  2                              :            46072
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:19.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45925
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869925
  j =  1                              :        399908156
  j =  2                              :            45913
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:28.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:17.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:45.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:59.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:54.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:33.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.45
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:48.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.02
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.83
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.47
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:40.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.80
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.11
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.40
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17509.73
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.99
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.86
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.56
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.18
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.66
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.30
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.23
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.79
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.34
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.58
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.39
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  416.01
p-value of test                       :    0.9974


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.29
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.23
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:46.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.95
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.39
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.76
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  170.72
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.49
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.93
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.86
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.03
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.59
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.04
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.89
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.94
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  435.17
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.13
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.24
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:20.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.65
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    3.14
p-value of test                       :  8.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.63e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 8.48e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.76
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.45
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.83
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:08.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:07.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9790.75
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9848.31
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.072
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:46.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5025.22
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4785.44
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.89
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.81
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.67
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11607.45
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.30
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000135259

Normal statistic for number of bits   :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.49
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999877091

Normal statistic for number of bits   :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -1.75
p-value of test                       :    0.96

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:20.96

 All tests were passed




Server wird beendet - Lösche Semaphor 103022606.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5368
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:49.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:46.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:07.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:23.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:23.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:05.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:37.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    2.27
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:12.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:40.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.01
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.33
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.08
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:35.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1390.57
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:59.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6989.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:40.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.32
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:03.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.84
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.89
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:33.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4851.64
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:06.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45423
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869423
  j =  1                              :        399909156
  j =  2                              :            45419
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46007
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870007
  j =  1                              :        399907990
  j =  2                              :            45999
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:32.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:27.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:55.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:10.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:54.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:22.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.30
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:33.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.64
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.31
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.86
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.76
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.05
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:03.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.14
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.01
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.3e-3

Anderson-Darling statistic = A2       :    4.27
p-value of test                       :  6.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  176.36
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17765.84
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.38
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.66
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.84
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.10
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.46
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.48
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.83
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.92
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.43
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.50
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.89
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.25
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.40
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.01
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.95
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.02
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.79
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.90
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.90
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.70
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.69
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.21
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.03
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.91
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.39
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.18
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.05
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.86
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.04
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.40
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:21.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.99
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :    1.38
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:19.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.94e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 3.93e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.67e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 5.04e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.48
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.93
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.91
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:07.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.89
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:08.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9860.96
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9876.83
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:50.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.23
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4257.08
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4016.02
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11944.81
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.70
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.07
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999938285

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.22
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999839072

Normal statistic for number of bits   :   -1.27
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 4.13e-3
p-value of test                       :    0.9957

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -2.05
p-value of test                       :    0.98

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:01.95

 All tests were passed




Server wird beendet - Lösche Semaphor 103809038.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5297
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:50.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:35.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:54.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4452
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:54.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:00.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:01.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:51.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:56.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.94
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    2.07
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.56
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:10.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    3.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:39.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.16
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.18
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.54
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.64
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.88
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.18
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.24
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:58.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6963.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.10
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.14
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:03.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.62
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.76
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5006.46
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:00.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46106
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870106
  j =  1                              :        399907788
  j =  2                              :            46106
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45796
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869796
  j =  1                              :        399908410
  j =  2                              :            45792
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:28.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.46
p-value of test                       :  5.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  4.5e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:19.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:44.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:54.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:32.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 8.15e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:35.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:35.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.93
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:47.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.55
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.81
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.45
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:47.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.06
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.26
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.41
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.01
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.32
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17566.68
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.65
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.44
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.82
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.74
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.85
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.96
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.95
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.40
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.92
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.63
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.43
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.81
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.08
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.22
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.58
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.74
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.08
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.22
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.70
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.58
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.15
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5133.71
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.53
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.70
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.15
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.45
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5143.77
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.17
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.55
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.65
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:22.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.74
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 5.39e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.48
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.81
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.25
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.57
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:05.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 2.40e-3
p-value of test                       :    0.9975

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9625.04
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.92
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:48.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.33
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3936.42
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11615.05
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11705.65
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.92
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999969872

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.96
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999862355

Normal statistic for number of bits   :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:09.37

 All tests were passed




Server wird beendet - Lösche Semaphor 104824846.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5406
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:52.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:37.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:00.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:01.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:53.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.21
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:45.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:10.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:39.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.13
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.82
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.84
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.37
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.32
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1353.16
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7059.70
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.31
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.45
p-value of test                       :    0.9940


-----------------------------------------------
CPU time used                    :  00:00:47.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.00
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:33.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5121.20
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:54.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46329
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870329
  j =  1                              :        399907345
  j =  2                              :            46323
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45620
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869620
  j =  1                              :        399908764
  j =  2                              :            45612
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:19.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:45.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:00.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:32.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.86e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    3.41
p-value of test                       :  3.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:35.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.30
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.77
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.54
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.99
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.21
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.93
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:37.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.12
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.69
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.33
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.72
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17751.35
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.21
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.81
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.14
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.93
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.56
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.03
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.54
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.92
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.06
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.72
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  440.34
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.63
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.39
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.81
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.70
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.03
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.37
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.09
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.31
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.02
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.86
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.73
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.46
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.80
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4887.90
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.55
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.10
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.96
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -2.02
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:21.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.94
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:21.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.79e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.41e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.22
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.80
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.17
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:05.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.78
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10214.01
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9828.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:50.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.05
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.02
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:50.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.50
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.06
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.37
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11832.93
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:30.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.76
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000066022

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.23
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999901694

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.5e-3

Anderson-Darling statistic = A2       :    3.87
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.35
p-value of test                       :  9.4e-3

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.86
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.59
p-value of test                       :  4.8e-3

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:29.32
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 56  SampleCorr, k = 2               3.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 105775118.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:56.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:38.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:54.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:02.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7151
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:03.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:57.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:45.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    3.39
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:09.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:40.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.03
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.06
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.99
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.82
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.50
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.27
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.66
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1550.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7037.30
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:42.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.02
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.32
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:04.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.98
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.93
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4964.65
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:58.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46209
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870209
  j =  1                              :        399907589
  j =  2                              :            46195
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46030
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870030
  j =  1                              :        399907945
  j =  2                              :            46020
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:20.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.47
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.97e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:33.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:32.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.72
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.81
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.22
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.13
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.77
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17557.33
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.89
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.53
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.69
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.83
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.66
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.63
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.44
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.45
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.45
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.18
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.02
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.00
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.37
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.29
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.91
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.24
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.95
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.39
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.94
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.87
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.27
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.49
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.67
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.91
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:34.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.52
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.91
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.46
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.01
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.88
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:20.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.18
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -1.65
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:20.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.38e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.25e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.38
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.14
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:05.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.68
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9825.98
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10145.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:42.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.72
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.09
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4370.57
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4384.82
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.44
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999951656

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.63
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999993824

Normal statistic for number of bits   :  -0.049
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.60
p-value of test                       :  2.7e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    4.36
p-value of test                       :  6.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.20
p-value of test                       :    0.99

Sample variance                       :    0.13
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:20.73

 All tests were passed




Server wird beendet - Lösche Semaphor 106790926.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:02.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:02.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:53.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:57.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:45.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.49
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     267
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:10.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     176
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:37.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.04
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.58
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.50
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.71
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.25
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.32
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.37
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.61
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1530.91
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6972.40
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.25
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:06.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.01
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.75
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:34.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5018.47
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:05.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45779
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869779
  j =  1                              :        399908443
  j =  2                              :            45777
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45694
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869694
  j =  1                              :        399908617
  j =  2                              :            45684
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:26.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:18.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 6.92e-3
p-value of test                       :    0.9921

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:55.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 8.78e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 6.07e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:34.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:33.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.45
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:47.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.71
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.00
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.74
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.67
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.95
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.85
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.14
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.87
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.51
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17431.42
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.86
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.48
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.08
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.90
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.95
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.47
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.48
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.91
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.33
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.58
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.85
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.08
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.49
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.47
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.80
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.62
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.54
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.64
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.07
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.06
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.17
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.15
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.06
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.78
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.31
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.01
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.16
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:21.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.63
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:20.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.60
p-value of test                       :    0.94

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 6.57e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.68e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 8.03e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.27
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.53
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.42
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:07.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9987.25
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.7e-3

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10261.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : -1.13e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:42.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.36
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:48.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5028.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.28
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.79
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.39
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11751.16
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.84
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000053851

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.33
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000043432

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:19.88

 All tests were passed




Server wird beendet - Lösche Semaphor 107806734.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:40.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:59.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:43.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:58.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:04.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:57.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:59.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.87
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     943
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:45.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:11.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:40.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.61
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.79
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.91
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.58
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.14
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.77
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.16
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1491.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7024.54
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.86
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.97
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:08.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.93
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.36
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:37.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5129.15
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:58.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45616
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869616
  j =  1                              :        399908768
  j =  2                              :            45616
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45779
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869779
  j =  1                              :        399908446
  j =  2                              :            45771
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:29.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:20.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9931

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:03.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:36.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 4.01e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.60e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.02
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.98
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.21
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.90
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.71
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.67
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.49
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17503.34
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.34
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.59
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.65
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.17
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.14
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.65
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.05
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.49
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.07
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.03
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.65
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.41
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.46
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.68
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.73
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.16
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.26
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.66
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.34
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.94
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.71
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.27
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.22
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.96
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.46
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.57
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5199.05
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.09
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.56
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.34
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:22.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.65
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:22.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.82e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.11
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.14
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.95
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:06.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.53
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:07.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9785.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10263.72
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:04:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.98
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:54.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4774.85
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.97
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12099.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:32.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11752.34
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:34.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.79
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000011761

Normal statistic for number of bits   :   0.093
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.58
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000095995

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.26
p-value of test                       :    0.99

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:33.70

 All tests were passed




Server wird beendet - Lösche Semaphor 108724238.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:40.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1502
p-value of test                       :  1.3e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334622
  j =  1                              :        599996996
  j =  2                              :             1502
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:57.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:02.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:03.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7532
p-value of test                       :  6.5e-3


-----------------------------------------------
CPU time used                    :  00:03:55.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:59.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:44.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:10.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.54
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.72
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.64
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.12
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.27
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.64
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.71
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.91
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.60
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.11
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:00.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7216.27
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.77
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.42
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:05.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.06
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.84
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5047.16
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:54.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45800
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869800
  j =  1                              :        399908402
  j =  2                              :            45796
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45932
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869932
  j =  1                              :        399908140
  j =  2                              :            45924
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:27.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:02.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:34.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 4.45e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.95e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.38
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:34.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:33.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:48.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.60
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.97
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.35
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:47.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.64
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.77
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.70
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.75
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.03
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.80
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17150.67
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.54
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.86
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.20
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.70
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.41
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.01
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.15
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.82
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.44
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.28
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.91
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.26
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.41
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.97
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.52
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.27
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.49
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.41
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.76
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.58
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.55
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.10
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.53
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.52
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.65
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.27
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.63
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.29
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   0.088
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:22.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.07
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -1.73
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:21.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9977

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.65e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.67e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 4.08e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.63
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.91
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.63
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:04.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.38
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:06.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.08
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.29
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:41.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9994    *****

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.41
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.37
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11917.64
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.64
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   83.84
p-value of test                       :  5.7e-3


-----------------------------------------------
Total number of bits:  7999848279

Normal statistic for number of bits   :   -1.20
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.10
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999969464

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:32.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           1.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 109805582.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5342
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:03.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:59.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.30
p-value of test                       :  6.4e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    2.04
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:11.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:37.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.15
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.38
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.28
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.21
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.90
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.25
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.78
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.59
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1368.08
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:02.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7214.32
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:05.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.37
p-value of test                       :    0.9961


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.49
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4860.14
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:52.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46132
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870132
  j =  1                              :        399907739
  j =  2                              :            46126
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45882
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869882
  j =  1                              :        399908241
  j =  2                              :            45872
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9962


-----------------------------------------------
CPU time used                    :  00:02:27.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:17.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:45.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:59.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.95e-4
p-value of test                       :  1.9e-3

Kolmogorov-Smirnov- statistic = D-    : 4.61e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.83
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 4.34e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:35.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.67
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:01:34.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.49
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.29
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.40
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:48.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.08
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.86
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.63
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.02
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17456.73
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.57
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.69
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.72
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.70
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.45
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.95
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.66
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.27
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.81
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.12
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.31
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.04
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.78
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.16
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.04
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.04
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  594.04
p-value of test                       :  2.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.78
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.95
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.78
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.65
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.77
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.06
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.59
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.93
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5138.30
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.38
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.99
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.63
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   -0.60
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:23.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.88
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :  -0.042
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.17
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.68e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 5.40e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.92
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.14
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:08.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.50
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9705.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10181.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:39.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.93
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.93
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.30
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11924.53
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11817.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.60
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000033868

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.81
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000097846

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 2.81e-3
p-value of test                       :    0.9971

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.17
p-value of test                       :    0.98

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.085
p-value of test                       :    0.53

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.95

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:56.65

 All tests were passed




Server wird beendet - Lösche Semaphor 110788622.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:59.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:43.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7145
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:04.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:04.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7498
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:59.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.29
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:12.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:40.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.83
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.37
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.00
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.69
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.50
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.42
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.79
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:43.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.90
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:02.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6962.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.63
p-value of test                       :  9.7e-3

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.15
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:05.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.97
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5213.34
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:56.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45457
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869457
  j =  1                              :        399909088
  j =  2                              :            45453
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45267
p-value of test                       :    0.9979


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869267
  j =  1                              :        399909466
  j =  2                              :            45267
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:27.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:17.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:44.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:58.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 7.90e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.12
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.87
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.23
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.02
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.78
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:37.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.08
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:39.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17316.47
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.99
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.36
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.24
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.84
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.21
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.50
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.80
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.61
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.14
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.27
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.44
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.59
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.91
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.07
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.96
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.58
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.56
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.86
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.07
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.62
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.01
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5100.64
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.74
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.43
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.47
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.75
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.92
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  438.15
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.76
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.99
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -1.47
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:22.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.16
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.95e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 7.35e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.50
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.52
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.27
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.39
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:06.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.03e-3
p-value of test                       :    0.9914

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  2.0e-3

Anderson-Darling statistic = A2       :    5.93
p-value of test                       :  1.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10482.20
p-value of test                       :  3.9e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9956.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:41.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.12
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.66
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:50.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.01
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.32
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.58
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11978.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.20
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999886418

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.69
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999981197

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:13.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 90  HammingWeight2, r = 0           3.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 111804430.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5253
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:58.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4226
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:05.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:56.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:00.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:45.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.47
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:13.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:37.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.61
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.61
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.55
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:29.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.19
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.36
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.82
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:44.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:02.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6892.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.66
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:04.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.62
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.71
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:31.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4945.08
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:55.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45844
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869844
  j =  1                              :        399908317
  j =  2                              :            45834
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45584
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869584
  j =  1                              :        399908837
  j =  2                              :            45574
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9935


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:25.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:17.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 7.97e-3
p-value of test                       :    0.9907

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.65e-4
p-value of test                       :  4.9e-3

Kolmogorov-Smirnov- statistic = D-    : 2.87e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    5.70
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:35.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.15
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.43
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.27
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.08
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:48.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.57
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.98
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.79
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:37.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.38
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.96
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.03
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.06
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17501.91
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.74
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.91
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.28
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.72
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.45
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.08
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.94
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.01
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.32
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.39
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.74
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.79
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.15
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.71
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.02
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.69
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.13
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.75
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.22
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.00
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.14
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4811.49
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.71
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.94
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.07
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.43
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4841.96
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.80
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  248.26
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.56
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:22.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.15
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :  -0.019
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:22.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.97e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 8.23e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.34
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.75
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:03.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.06
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:05.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10188.50
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.33
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.045
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.027
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:42.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9920

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.76
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:50.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.98
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4277.15
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11981.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11745.73
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:29.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.56
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999862499

Normal statistic for number of bits   :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.23
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999875150

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.84
p-value of test                       :    0.97

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:44.20

 All tests were passed




Server wird beendet - Lösche Semaphor 112820238.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:58.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7533
p-value of test                       :  6.3e-3


-----------------------------------------------
CPU time used                    :  00:02:42.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:06.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:56.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:00.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.06
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    3.59
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     856
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:14.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    7.08
p-value of test                       :  3.5e-4    *****

Test on the Nm values of W_{n,i}(mNP1):    2.98
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     126
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:42.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.71
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.98
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.33
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.85
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.75
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.32
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  361.62
p-value of test                       :    0.9951

-----------------------------------------------
CPU time used                    :  00:01:44.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.04
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6876.09
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:45.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.20
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.85
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:05.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.89
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.53
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:33.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5083.87
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:56.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45667
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869667
  j =  1                              :        399908666
  j =  2                              :            45667
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45798
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869798
  j =  1                              :        399908410
  j =  2                              :            45786
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:25.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:17.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:01.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:54.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 6.49e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.55e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:34.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:33.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.50
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.36
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.77
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.18
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.74
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.93
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.64
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.82
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17411.52
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.11
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.05
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.86
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.06
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.45
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.32
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.14
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.03
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   43.64
p-value of test                       :  8.4e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.37
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.88
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.24
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.55
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.33
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.71
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.17
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.20
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.04
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.92
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  109.44
p-value of test                       :  4.7e-3


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  323.77
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.74
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.23
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.47
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  158.80
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.52
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.49
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5144.99
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  434.91
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.98
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.19
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:21.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.41
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -1.40
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:21.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.37e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.26e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.17e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.83
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.85
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.18
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.84
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:06.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9748.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.76
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:37.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:47.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:50.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.12
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12085.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.34
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999877595

Normal statistic for number of bits   :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.64
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000041815

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :  1.0e-3    *****

Anderson-Darling statistic = A2       :    6.30
p-value of test                       :  7.6e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :    3.22
p-value of test                       :  6.5e-4    *****

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.00
p-value of test                       :    0.98

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:07.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP, t = 16          3.5e-4
 104  AutoCor, d=3, r=0               6.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 113836046.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:59.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7503
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7161
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:07.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:07.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:57.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:02.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    3.86
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:16.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:44.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.72
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.43
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.15
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.05
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.48
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.33
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.73
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.01
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1374.79
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:04.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7092.99
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:45.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.01
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.41
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:02.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.52
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.82
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4977.30
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:53.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46045
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870045
  j =  1                              :        399907914
  j =  2                              :            46037
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45965
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869965
  j =  1                              :        399908074
  j =  2                              :            45957
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:25.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:19.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:02.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:33.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 6.80e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:35.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:34.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.26
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.78
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.28
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:48.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.22
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.79
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.02
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:37.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.60
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.11
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17378.49
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.72
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.78
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.65
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.67
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.99
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.94
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.27
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.84
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.29
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.18
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.88
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.35
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.41
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.30
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.76
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.25
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.61
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.75
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.38
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.50
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.70
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.15
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5092.53
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.03
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.71
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.88
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.37
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5192.71
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.87
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.68
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.02
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:23.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.04
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -1.25
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 4.29e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.90
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.33
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.21
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9866.50
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9972.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:40.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9922

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.76
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.41
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:50.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.20
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4005.17
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11737.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12328.22
p-value of test                       :  6.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.86
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999973355

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.39
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999827639

Normal statistic for number of bits   :   -1.36
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         : 9.56e-3
p-value of test                       :    0.50

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:41.85
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 100  HammingIndep, L=1200, r=25      6.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 114851854.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:57.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:45.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4175
p-value of test                       :    0.9931


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:07.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:07.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:57.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:02.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.14
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     849
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.23
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:16.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:42.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.92
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.43
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.73
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.38
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1400.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:02.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7304.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.11
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:03.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.67
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.68
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5215.55
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:56.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46092
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870092
  j =  1                              :        399907819
  j =  2                              :            46086
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45848
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869848
  j =  1                              :        399908308
  j =  2                              :            45840
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:26.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:17.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:44.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:54.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.83e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.40
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.44
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.62
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.68
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.08
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.20
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.38
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.17
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.67
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  166.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17146.57
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.56
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.23
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.12
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.05
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.38
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.04
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.00
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.28
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.96
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.29
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.36
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.42
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.50
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.37
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.42
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.87
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.16
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.50
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.58
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.47
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.53
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.71
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.38
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.27
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.20
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.21
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.64
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.66
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.09
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.19
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.71
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   -1.54
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.14e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 5.53e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.73
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.91
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.44
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.81
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10103.71
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10142.67
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:40.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5015.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3953.55
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3981.96
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11516.56
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11702.78
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.84
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000095884

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.14
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000154246

Normal statistic for number of bits   :    1.22
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         : 7.22e-3
p-value of test                       :    0.50

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:24.95

 All tests were passed




Server wird beendet - Lösche Semaphor 115834894.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:02.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:02.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5548
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:57.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:43.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:59.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:09.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:03.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:14.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:43.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.81
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.98
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.61
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  265.03
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.82
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:44.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1580.25
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:02:01.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6992.72
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:44.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:03.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.68
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.09
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:32.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4996.24
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:57.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46328
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870328
  j =  1                              :        399907349
  j =  2                              :            46318
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45936
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869936
  j =  1                              :        399908136
  j =  2                              :            45920
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:26.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:17.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.14
p-value of test                       :  7.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9971


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 9.90e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :  4.3e-3

Anderson-Darling statistic = A2       :    5.18
p-value of test                       :  2.4e-3


-----------------------------------------------
CPU time used                    :  00:01:58.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:54.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 8.03e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:33.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:48.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.64
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:48.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.61
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.23
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.30
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.36
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.94
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17377.23
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.46
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.63
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.95
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.47
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.16
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.12
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.63
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.53
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.97
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.34
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.76
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.01
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.54
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.64
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.07
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.26
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  113.21
p-value of test                       :  2.3e-3


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.06
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.35
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5141.54
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  316.04
p-value of test                       :    0.9910


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.79
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.87
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.64
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.21
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.07
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.31
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.97
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :    0.57
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:20.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.46
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    1.35
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:21.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.29
p-value of test                       :    0.01

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 5.63e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 6.98e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.54
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.10
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.05
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:06.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.28
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:05.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9869.86
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.65
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9636.50
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:39.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.00
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4756.95
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:49.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.62
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4273.03
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12016.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11727.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.76
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000016312

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.32
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999953060

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   0.091
p-value of test                       :    0.46

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:49.28

 All tests were passed




Server wird beendet - Lösche Semaphor 116850702.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:43.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:08.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:08.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:57.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:01.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:53.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    2.19
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    4.53
p-value of test                       :  4.8e-3

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:15.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:45.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.45
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.24
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.42
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.27
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.94
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:44.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1314.61
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:02:02.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7036.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.68
p-value of test                       :  4.1e-3

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.11
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:03.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.90
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.82
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5008.27
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:57.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45762
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869762
  j =  1                              :        399908481
  j =  2                              :            45752
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45623
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869623
  j =  1                              :        399908757
  j =  2                              :            45617
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.40e-3
p-value of test                       :    0.9961

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:27.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:17.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:54.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.77e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.069
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:33.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.10
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.95
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.28
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:37.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.57
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.27
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17585.13
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.27
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.29
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.51
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.90
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.71
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.41
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.50
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.48
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.76
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.03
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.27
p-value of test                       :    0.9944


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.54
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.33
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.73
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.55
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.41
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.69
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.35
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.61
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.72
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4861.22
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.26
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.41
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.48
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.09
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4931.33
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.71
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  245.35
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.04
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :    1.45
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:21.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.42
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.32e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 4.42e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.01
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.99
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.60
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:05.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 8.39e-3
p-value of test                       :    0.9910

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:04.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10107.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:38.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.55
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.29
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4295.32
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11597.04
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.95
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999998429

Normal statistic for number of bits   :  -0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.87
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999864566

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    2.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:46.05

 All tests were passed




Server wird beendet - Lösche Semaphor 117833742.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:39.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1265
p-value of test                       :    0.9966

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334385
  j =  1                              :        599997470
  j =  2                              :             1265
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5431
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:58.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:42.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:06.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:57.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:01.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:51.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     548
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    2.70
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:17.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    2.53
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:42.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   25.09
p-value of test                       :  7.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.39
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.48
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   28.74
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.28
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.39
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  265.43
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.03
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1538.66
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6955.40
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:43.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.10
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.62
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:02.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.46
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.97
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4889.90
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:57.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45993
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869993
  j =  1                              :        399908020
  j =  2                              :            45981
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46029
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870029
  j =  1                              :        399907943
  j =  2                              :            46027
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

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CPU time used                    :  00:04:53.19

Generator state:




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HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


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CPU time used                    :  00:02:26.92

Generator state:




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HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


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CPU time used                    :  00:02:16.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


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CPU time used                    :  00:01:43.89

Generator state:




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HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


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CPU time used                    :  00:01:59.11

Generator state:




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HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

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CPU time used                    :  00:01:54.07

Generator state:




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HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

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CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

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CPU time used                    :  00:01:33.52

Generator state:




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HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.92e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 2.88e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

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CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

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CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
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   N =  1,  n = 2000000000,  r =  0,   k = 1


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Normal statistic                      :    0.85
p-value of test                       :    0.20

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CPU time used                    :  00:00:22.31

Generator state:




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HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


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Normal statistic                      :   -0.21
p-value of test                       :    0.58

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CPU time used                    :  00:00:22.39

Generator state:




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HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

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CPU time used                    :  00:01:33.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.27
p-value of test                       :    0.01

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CPU time used                    :  00:01:34.09

Generator state:




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HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


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Number of degrees of freedom          :   67
Chi-square statistic                  :   76.17
p-value of test                       :    0.21

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CPU time used                    :  00:00:48.35

Generator state:




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HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


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Number of degrees of freedom          :   67
Chi-square statistic                  :   75.43
p-value of test                       :    0.22

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CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


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Number of degrees of freedom          :   67
Chi-square statistic                  :   60.24
p-value of test                       :    0.71

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CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.30
p-value of test                       :    0.50

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CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.80
p-value of test                       :    0.39

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CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


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Number of degrees of freedom          :   37
Chi-square statistic                  :   56.34
p-value of test                       :    0.02

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CPU time used                    :  00:00:51.61

Generator state:




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HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


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Number of degrees of freedom          :   29
Chi-square statistic                  :   23.18
p-value of test                       :    0.77

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CPU time used                    :  00:01:38.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.74
p-value of test                       :    0.93

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CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.73
p-value of test                       :    0.79

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CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


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Number of degrees of freedom          :    3
Chi-square statistic                  :   10.92
p-value of test                       :    0.01

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CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.56
p-value of test                       :    0.02

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CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


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Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

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CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


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Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

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CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.03
p-value of test                       :    0.48

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CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17166.01
p-value of test                       :    0.92



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CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.20
p-value of test                       :    0.9941


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Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.78
p-value of test                       :    0.39


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Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.35
p-value of test                       :    0.62


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Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.32
p-value of test                       :    0.68


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Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.34
p-value of test                       :    0.71


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CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.62
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.42
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.22
p-value of test                       :    0.79


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Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.19
p-value of test                       :    0.85


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CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.71
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.89
p-value of test                       :    0.11


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Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.54
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.66
p-value of test                       :    0.37


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Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.76
p-value of test                       :    0.02


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CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.75
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.82
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.08
p-value of test                       :    0.08


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Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.12
p-value of test                       :    0.67


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CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.92
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.12
p-value of test                       :    0.71


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Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.18
p-value of test                       :    0.17


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Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.76
p-value of test                       :    0.07


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Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.91
p-value of test                       :    0.59


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CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.75
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.49
p-value of test                       :    0.31


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Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4909.26
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.98
p-value of test                       :    0.05


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Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.29
p-value of test                       :    0.81


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CPU time used                    :  00:00:34.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.17
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -0.47
p-value of test                       :    0.68



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CPU time used                    :  00:02:21.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.49
p-value of test                       :    0.49


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Normal statistic for number of jumps  :   -0.19
p-value of test                       :    0.58



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CPU time used                    :  00:02:22.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.23

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.19e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 5.61e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 6.65e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.51
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.85
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:04.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:05.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9891.43
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10183.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.093
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:40.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.70
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.60
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.44
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.43
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11952.79
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11801.78
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:29.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.94
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000049126

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.35
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999964598

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:13.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 27  SimpPoker, r = 27               7.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 118882318.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5393
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:54.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:07.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7496
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:05.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:56.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:01.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:51.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:17.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.96
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    4.06
p-value of test                       :  8.2e-3

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:51.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.41
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.47
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.29
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  265.10
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  474.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1343.06
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:01.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7043.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:43.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.05
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:03.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.20
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.47
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:32.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5194.16
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  6.5e-3


-----------------------------------------------
CPU time used                    :  00:03:07.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45943
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869943
  j =  1                              :        399908118
  j =  2                              :            45935
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45842
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869842
  j =  1                              :        399908321
  j =  2                              :            45832
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:27.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:18.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:59.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:59.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.90e-3
p-value of test                       :    0.9921

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:40.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.89e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.25e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:31.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:32.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.17
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.21
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.86
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:38.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.16
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   97.78
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17490.23
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.34
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.68
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.43
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.47
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.20
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.47
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.44
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.46
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.27
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.39
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.28
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.19
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.26
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.62
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.85
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.00
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.58
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.50
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.92
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.38
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.75
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.07
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.55
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.35
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.61
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.01
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5126.53
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.17
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.35
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.72
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -1.06
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:20.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.17
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -1.68
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:20.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    1.85
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.81e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 9.81e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.28
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.77
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.64
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:03.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.40
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10074.62
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.86
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:40.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:47.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4745.84
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:50.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.58
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4198.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.28
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.44
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999937766

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.60
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000321823

Normal statistic for number of bits   :    2.54
p-value of test                       :  5.5e-3



-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    2.36
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-3
p-value of test                       :    0.9986

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    2.09
p-value of test                       :    0.02

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:52.70

 All tests were passed




Server wird beendet - Lösche Semaphor 119865358.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5445
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:59.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:00.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:04.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:20.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:48.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7460
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:46.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:26.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:05:14.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9950

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    3.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:50.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    2.00
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:20.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:47.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.14
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.32
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.64
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.09
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.64
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.52
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.58
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:30.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:33.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7024.28
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:36.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.40
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:02.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.24
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.73
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:32.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5224.22
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:00.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46002
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870002
  j =  1                              :        399907997
  j =  2                              :            46000
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46141
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870141
  j =  1                              :        399907723
  j =  2                              :            46131
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:26.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:23.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:52.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:07.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:34.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:31.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:32.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.71
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.91
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.00
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.89
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:47.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.96
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:33.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.87
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.48
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:39.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17494.23
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.77
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.60
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.69
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.68
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.21
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.78
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.43
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.83
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.49
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.26
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.55
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.65
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.26
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.98
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.45
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.33
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.69
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.70
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.59
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.13
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.24
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.34
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4852.39
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.77
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.99
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.84
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.58
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.45
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.12
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.11
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.56
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:20.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.10
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:21.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.27e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 2.45e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.13
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.65
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.01
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:06.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.15
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:06.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9822.73
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10063.88
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:37.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.81
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.14
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4018.02
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11785.80
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11590.51
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:29.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.37
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000032842

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.96
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999960092

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:48.29

 All tests were passed




Server wird beendet - Lösche Semaphor 120881166.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:41.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:35.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:34.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:54.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:54.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:00.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:00.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:52.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:58.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    4.40
p-value of test                       :  5.6e-3

Stat. AD after spacings (mNP2-S)      :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.46
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:10.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    2.71
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    2.68
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:36.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.14
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.26
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.12
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.96
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.57
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.89
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.24
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:53.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.88
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7138.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9929

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.09
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.89
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:02.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.03
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.09
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:35.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5095.65
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:12.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45788
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869788
  j =  1                              :        399908428
  j =  2                              :            45780
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46204
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870204
  j =  1                              :        399907595
  j =  2                              :            46198
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:29.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:19.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  3.6e-3

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:34.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:34.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.87
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.64
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.81
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.87
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:46.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.45
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17188.97
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.23
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.64
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.08
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.56
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:39.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.82
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.21
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.16
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.07
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.08
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.81
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.54
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.24
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.42
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.40
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.67
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.38
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.23
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.31
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.74
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.31
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.18
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5169.96
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.85
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.32
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.23
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.25
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.60
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.68
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.36
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.48
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:17.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.93
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -1.36
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:16.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.90
p-value of test                       :    0.03

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 9.78e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.32e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.57
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.54
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.13
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:08.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:09.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9889.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9737.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:41.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4979.00
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4762.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:49.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.27
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4274.22
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11668.55
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11842.01
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.82
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999997451

Normal statistic for number of bits   :  -0.020
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.04
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000071893

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:14:16.39

 All tests were passed




Server wird beendet - Lösche Semaphor 102072335.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:40.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5320
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:43.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:35.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:54.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:01.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:01.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:52.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:58.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.36
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:11.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:40.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.52
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.58
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.19
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.10
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.56
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.57
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:43.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.43
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6984.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.82
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:05.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.45
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:47.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.72
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5002.20
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:17.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45752
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869752
  j =  1                              :        399908497
  j =  2                              :            45750
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45588
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869588
  j =  1                              :        399908827
  j =  2                              :            45582
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:28.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:18.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :  3.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:45.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:53.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:32.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.69e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:36.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:47.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.49
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:47.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.96
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.39
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.37
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.32
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17721.42
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.82
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.89
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.84
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.09
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.69
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.08
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.22
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.54
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.78
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.16
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.78
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.55
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.35
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.59
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.04
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.62
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.79
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.62
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.85
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.88
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.08
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.17
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.30
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.78
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.28
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:34.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  456.91
p-value of test                       :  6.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.63
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.21
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.48
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.60
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:34.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.73
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:18.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.56
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -1.68
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:18.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    2.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 8.45e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.56e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.27
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.32
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.45
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:07.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.44
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.14
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.074
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:54.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5000.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.41
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:50.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4239.13
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.36
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11969.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11767.83
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.94
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999906914

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.19
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999954971

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :  -0.074
p-value of test                       :    0.53

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :  -0.040
p-value of test                       :    0.52

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:48.96

 All tests were passed




Server wird beendet - Lösche Semaphor 102989839.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:45.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:37.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:54.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:54.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7462
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:00.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:01.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:53.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:56.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.01
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:11.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.11
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:38.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.03
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.76
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.28
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.21
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.47
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.93
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  193.54
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.52
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.81
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7038.13
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.55
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.40
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:07.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.03
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.08
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:32.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5076.65
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46074
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870074
  j =  1                              :        399907856
  j =  2                              :            46066
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45874
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869874
  j =  1                              :        399908257
  j =  2                              :            45864
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:27.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:17.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:59.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:54.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : -8.61e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:33.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.26
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.18
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.89
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:48.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.84
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.59
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:41.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17338.32
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.78
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.06
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.60
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.02
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.26
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.74
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.20
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.74
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.67
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.64
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.45
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.60
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.19
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.41
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.64
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.49
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.49
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.60
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.62
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.73
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.36
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5094.93
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.35
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.79
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.14
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.78
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.37
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.59
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.24
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.53
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -1.39
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:19.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.06
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :  -0.060
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:18.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:11.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.22e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.23e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.08
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.82
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.25
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:08.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10073.87
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.87
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:42.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.93
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.77
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.82
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.21
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999969152

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.82
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000020611

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :  -0.052
p-value of test                       :    0.52

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:57.69

 All tests were passed




Server wird beendet - Lösche Semaphor 104005647.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:51.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5494
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:50.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:36.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:35.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:53.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:55.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:01.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:02.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:54.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:55.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.04
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.30
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.69
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    4.09
p-value of test                       :  7.9e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    3.05
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.35
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    2.75
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     356
p-value of test                       :  9.0e-4    *****

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:10.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:39.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.63
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.12
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.92
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.29
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.01
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.16
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  494.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.31
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:05.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7111.60
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.14
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:10.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.69
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.22
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4944.69
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:19.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45937
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869937
  j =  1                              :        399908131
  j =  2                              :            45927
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46161
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870161
  j =  1                              :        399907684
  j =  2                              :            46149
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.69e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:30.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:19.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :  2.4e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 6.31e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    6.43
p-value of test                       :  6.4e-4    *****


-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.79e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.092
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:45.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.90
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.09
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.65
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.89
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17506.02
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.38
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.22
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.49
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.62
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.94
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.51
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.73
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.96
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.67
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.31
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.36
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.43
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.96
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.05
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.38
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.03
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.78
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.65
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.67
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.15
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4915.32
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.81
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.93
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.39
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.51
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.09
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.76
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.51
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.28
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:22.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.84
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :    2.92
p-value of test                       :  1.8e-3



-----------------------------------------------
CPU time used                    :  00:02:24.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.95e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.25
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.86
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.71
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.20
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.33
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9958.31
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:04:21.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.03
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:52.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.33
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:54.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.75
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11863.41
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:32.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11667.86
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:32.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.48
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000094372

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.41
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000071380

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:30.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs NJumps, t = 9        9.0e-4
 49  MaxOft AD, t = 32               6.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 104792079.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  2.5e-3


-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1263
p-value of test                       :    0.9971

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334383
  j =  1                              :        599997474
  j =  2                              :             1263
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1267
p-value of test                       :    0.9959

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334387
  j =  1                              :        599997466
  j =  2                              :             1267
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5392
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:47.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:38.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:37.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:03.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:03.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:51.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:57.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     953
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9944

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    5.34
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:11.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    3.91
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:02:39.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.72
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.77
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.99
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.23
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.73
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.34
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:46.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1502.51
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:59.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7081.75
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.58
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:02.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.03
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.86
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4821.75
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:03.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45643
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869643
  j =  1                              :        399908716
  j =  2                              :            45639
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45962
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869962
  j =  1                              :        399908078
  j =  2                              :            45958
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:27.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:01.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:55.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.17e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:35.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:34.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:47.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.29
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.41
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:47.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.14
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:39.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.90
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.23
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17251.28
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.48
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.04
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.34
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.60
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.64
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.08
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.93
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.51
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.01
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.96
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.67
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.38
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.25
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.69
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.78
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.13
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.02
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.66
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.12
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.41
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.17
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5168.72
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.55
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.40
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.65
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.43
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.20
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.97
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.58
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.06
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    1.48
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:23.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.77
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:22.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 3.93e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.47e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.31
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.98
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.59
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:08.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:09.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.16
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.16
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:39.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.23
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.05
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.65
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11675.53
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.18
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999946661

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.20
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999901118

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   0.081
p-value of test                       :    0.47

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:06.93

 All tests were passed




Server wird beendet - Lösche Semaphor 106004495.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9990


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:48.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:38.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:37.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:03.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:03.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:52.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:59.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.14
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.63
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:45.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    3.17
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.88
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:12.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:39.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.38
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.65
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.74
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.21
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.83
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  184.74
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.85
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6914.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:41.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.45
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:03.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.70
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.04
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5219.14
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:02.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908192
  j =  2                              :            45895
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45278
p-value of test                       :    0.9975


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869278
  j =  1                              :        399909448
  j =  2                              :            45270
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  4.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 3.01e-3
p-value of test                       :    0.9966

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:29.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:17.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:55.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:32.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 5.65e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.35e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:33.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.92
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:47.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.10
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.44
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.55
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.55
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:39.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.63
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.93
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  161.32
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17350.07
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.07
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.77
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.79
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.36
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.14
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.64
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.46
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.79
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.53
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.23
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.83
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.91
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.06
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.54
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.62
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.35
p-value of test                       :  7.0e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  574.28
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.74
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.33
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.17
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.47
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.68
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.79
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.46
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.07
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.38
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.72
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.15
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.87
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.48
p-value of test                       :    0.9982


-----------------------------------------------
Normal statistic for number of jumps  :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.83
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :   -1.45
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:25.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.90e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 9.98e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.85
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.63
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.57
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:07.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.02
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:05.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9825.39
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.20
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:39.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5014.78
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:48.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.98
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:49.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.13
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.08
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11601.66
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.62
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.74
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999901388

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.81
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999987596

Normal statistic for number of bits   :  -0.098
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:39.55

 All tests were passed




Server wird beendet - Lösche Semaphor 106954767.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:51.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5370
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:50.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:37.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7188
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:02.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:02.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:52.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:58.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9962

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    3.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:12.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.84
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.85
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.05
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.56
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.15
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:58.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7103.53
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:41.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.00
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9909

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.25
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:03.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.36
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:46.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.91
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:33.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5047.51
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:59.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45768
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869768
  j =  1                              :        399908468
  j =  2                              :            45760
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45522
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869522
  j =  1                              :        399908959
  j =  2                              :            45516
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:27.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:17.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:58.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:33.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 5.44e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.031
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:34.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:47.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.90
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.92
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.50
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:38.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.39
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.18
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.60
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17463.79
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.58
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.74
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.86
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.35
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.57
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.78
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.48
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.36
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.50
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.09
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.21
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.52
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.32
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.41
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.09
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.07
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.76
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.50
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.58
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  464.43
p-value of test                       :  3.0e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.48
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.41
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.47
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.41
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.88
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.81
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.43
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.82
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  241.97
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.54
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.65
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:25.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.34e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.71
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.76
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.15
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.11
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:07.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.15
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10025.47
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:41.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5015.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.48
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.33
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.00
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11987.54
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.45
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999890897

Normal statistic for number of bits   :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.33
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000081910

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   0.096
p-value of test                       :    0.46

Sample variance                       :    2.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:00.64

 All tests were passed




Server wird beendet - Lösche Semaphor 107937807.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1222
p-value of test                       : 1 -  4.8e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334342
  j =  1                              :        599997556
  j =  2                              :             1222
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5348
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:53.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:38.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:55.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:02.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:03.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:55.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:04:00.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:13.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.32
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.75
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.15
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.25
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.53
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.13
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  198.10
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7056.99
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.92
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:04.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.60
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.22
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:33.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4944.16
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46138
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870138
  j =  1                              :        399907725
  j =  2                              :            46136
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45994
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869994
  j =  1                              :        399908015
  j =  2                              :            45988
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :  5.6e-4    *****

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:28.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:18.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:44.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:59.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:35.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.49
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:47.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.59
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.35
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.33
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:46.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.24
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.18
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   46.91
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.50
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.34
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.10
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.16
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.30
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17488.72
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.44
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.59
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.59
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.37
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.67
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.53
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.71
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.10
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.69
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.56
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.24
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.60
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  570.28
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.59
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.84
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.71
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.74
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.30
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.22
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.11
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.22
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.85
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.55
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.16
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.20
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.31
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.51
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4860.92
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.15
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.45
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :    1.18
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.99
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:24.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-3
p-value of test                       :    0.9904

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.46e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.38
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.37
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.33
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:04.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.67
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:04.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9800.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.51
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:43.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.65
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:50.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4259.01
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.11
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11942.80
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12007.45
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.55
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999949763

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.05
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000075532

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    2.65
p-value of test                       :  4.5e-3

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:25.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  4  CollisionOver, t = 2           1 -  4.8e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 108855311.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1227
p-value of test                       : 1 -  8.4e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334347
  j =  1                              :        599997546
  j =  2                              :             1227
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5433
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:58.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7536
p-value of test                       :  5.7e-3


-----------------------------------------------
CPU time used                    :  00:02:42.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4474
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:59.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:10.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:07.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:09.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.21
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:13.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    2.02
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     125
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9905

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:42.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.30
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.11
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.96
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.56
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.84
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.40
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:09.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6910.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:59.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.52
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.97
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:19.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.74
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.28
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5078.51
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:05.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45409
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869409
  j =  1                              :        399909185
  j =  2                              :            45403
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45924
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869924
  j =  1                              :        399908160
  j =  2                              :            45908
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:31.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:21.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:11.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:58.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.67e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.32e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:52.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:53.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.70
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.19
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.47
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:52.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.09
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.18
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.21
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17443.54
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.38
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.17
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.78
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.58
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.29
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.72
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.13
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.70
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.39
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.02
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.13
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.73
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.24
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.26
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.94
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.07
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.62
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.74
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.19
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.67
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.03
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5109.93
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.36
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.78
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.48
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.89
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.88
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.62
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.09
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   0.092
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:23.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.64
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -1.67
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:25.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.48e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 7.17e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 6.50e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.42
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.13
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:06.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.60
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10043.79
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9967.43
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:04:34.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9978

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.52
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.14
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.46
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.67
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:36.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.79
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999923879

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.24
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999979349

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    3.65
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.32
p-value of test                       :    0.01

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         : -8.60e-3
p-value of test                       :    0.50

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:44.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21          1 -  8.4e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 109871119.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5369
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:56.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:53.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:01.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:12.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:32.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:32.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:10.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:52.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:12.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.75
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.29
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.50
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.84
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.35
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.06
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1524.17
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:06.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6957.46
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.07
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:09.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.44
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.61
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:37.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.46
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:01.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46105
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870105
  j =  1                              :        399907793
  j =  2                              :            46099
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45807
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869807
  j =  1                              :        399908388
  j =  2                              :            45803
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:36.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:34.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:03.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:21.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.03e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:45.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.40
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.08
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.84
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.84
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.47
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.63
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.08
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.00
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17280.10
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.83
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.39
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.76
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.41
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.49
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.85
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.85
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.39
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.32
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.21
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.76
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.47
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.71
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.87
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.66
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.24
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.85
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.10
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.12
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.39
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.37
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4819.44
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.10
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.23
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.86
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.24
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.48
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.26
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.27
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.96
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:24.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.15
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   -1.41
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 3.34e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.56e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.94
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.34
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.68
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10141.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9817.09
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:04:17.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:53.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.45
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.08
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4262.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12255.84
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11685.35
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.11
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000077125

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.67
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999942149

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:07.70

 All tests were passed




Server wird beendet - Lösche Semaphor 111214607.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5518
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:51.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:39.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:04.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:55.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:00.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     644
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    3.36
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:12.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.21
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.57
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.14
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.61
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.14
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.15
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.34
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.91
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.59
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1501.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:01.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6959.82
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.08
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.70
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:02.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.32
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.04
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4964.87
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:54.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46142
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870142
  j =  1                              :        399907720
  j =  2                              :            46134
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908376
  j =  2                              :            45800
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:27.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:18.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:45.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:01.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.68e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.73e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:33.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:33.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.31
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.35
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.77
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.75
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.77
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.40
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.75
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17444.73
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.67
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.47
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.62
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.68
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.27
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.68
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.28
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.21
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.38
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.83
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.22
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.06
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.02
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.94
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.57
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.35
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.58
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.10
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.26
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.54
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.49
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.60
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5143.68
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.39
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.91
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.07
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.73
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.33
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.31
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.89
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -1.50
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:24.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.39
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:23.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :  -0.098
p-value of test                       :    0.54

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.74e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 9.90e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.40
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.80
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.03
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:05.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
p-value of test                       :    0.9920

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  250.71
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:02:06.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.35
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10179.32
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:42.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5034.56
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.05
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11591.31
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11580.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.56
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000048013

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.60
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000025852

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    2.44
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:37.42

 All tests were passed




Server wird beendet - Lösche Semaphor 112328719.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5472
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:53.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4202
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:55.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    2.25
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    3.00
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:45.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:11.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:41.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.63
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.36
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.92
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.71
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.45
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.93
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:01.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7131.34
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.64
p-value of test                       :  7.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.92
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   13.57
p-value of test                       :    0.9957

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:03.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.40
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   91.68
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4972.05
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:56.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45944
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869944
  j =  1                              :        399908117
  j =  2                              :            45934
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45871
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869871
  j =  1                              :        399908259
  j =  2                              :            45869
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:27.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:01.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:55.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:33.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 4.43e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.76e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.047
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.35
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:48.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.77
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.94
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.20
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.01
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:38.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.19
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17518.35
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.83
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.18
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.51
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.94
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.04
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.34
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.16
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.88
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.11
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.11
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.59
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.39
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.65
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.67
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.69
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.56
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  441.12
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.08
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.00
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.06
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.68
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.10
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.24
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.64
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.65
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.90
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.21
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  441.84
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.98
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.79
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :  -0.086
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:22.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.42
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.15e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.14
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.00
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.08
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.18
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.59
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10106.22
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:40.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.64
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.79
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:50.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.37
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4257.89
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11842.21
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11683.89
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.06
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999986804

Normal statistic for number of bits   :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.52
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000102352

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.77e-3
p-value of test                       :    0.9928

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.86
p-value of test                       :    0.97

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:09.90

 All tests were passed




Server wird beendet - Lösche Semaphor 113246223.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:50.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1233
p-value of test                       :    0.9998    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334353
  j =  1                              :        599997534
  j =  2                              :             1233
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:53.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:04.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:03.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:53.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:58.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:44.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:10.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:41.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.64
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.70
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.59
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.46
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.73
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1492.73
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:01.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7068.77
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:41.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.71
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:04.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.39
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   91.31
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:33.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5103.85
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:55.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45685
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869685
  j =  1                              :        399908633
  j =  2                              :            45679
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45914
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869914
  j =  1                              :        399908174
  j =  2                              :            45910
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:27.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:17.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:45.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :  9.9e-4    *****

Anderson-Darling statistic = A2       :    3.74
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:34.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.83e-4
p-value of test                       :  2.9e-3

Kolmogorov-Smirnov- statistic = D-    : 1.12e-5
p-value of test                       :    0.9950

Anderson-Darling statistic = A2       :    5.31
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.45
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.40
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.01
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.00
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:48.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.34
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:37.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.51
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.23
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17168.31
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.63
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.67
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.15
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.94
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.78
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.42
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.37
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.37
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.29
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.12
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.05
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.69
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.18
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.85
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.33
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.06
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  438.48
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.94
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.12
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.32
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.69
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5037.40
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  327.86
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.63
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.44
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.61
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.63
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.07
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.15
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.60
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:22.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.67
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    1.35
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:22.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 6.23e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.71
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.99
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.64
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:04.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.62
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:05.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.00
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10328.47
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.022
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:40.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.53
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.97
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4236.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12073.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11773.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.33
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999981737

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.63
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999789932

Normal statistic for number of bits   :   -1.66
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.97
p-value of test                       :    0.02

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    2.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:05.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 114065423.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  2.1e-3


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:56.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7507
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:03.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:54.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:58.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.58
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:45.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:10.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.10
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.65
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.05
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.78
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.60
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.29
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.05
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.82
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:04.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6962.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.70
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.04
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:04.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.50
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.78
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:33.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4946.60
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:56.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46210
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870210
  j =  1                              :        399907588
  j =  2                              :            46194
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45605
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869605
  j =  1                              :        399908790
  j =  2                              :            45605
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:26.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.22e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.78
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  3.9e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.71e-3
p-value of test                       :    0.9946

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:17.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :  2.0e-3

Anderson-Darling statistic = A2       :    3.93
p-value of test                       :  9.7e-3


-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.23e-3
p-value of test                       :    0.9930

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.19
p-value of test                       :  7.2e-3

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 7.12e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.80e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 9.98e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.78
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.65
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.69
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.02
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.24
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.36
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.21
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17388.49
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.67
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.75
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.68
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.13
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.78
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.98
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.65
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.68
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.24
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.81
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.24
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.00
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.73
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.99
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.09
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.48
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.98
p-value of test                       :  6.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.32
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.30
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.19
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.56
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.26
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4909.58
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.36
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.29
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.49
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.81
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4831.28
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.48
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.36
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.37
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:24.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.57
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    0.51
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:24.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.098
p-value of test                       :    0.46

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.82e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.29
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.36
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.56
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:04.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.21
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:05.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9830.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.91
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : 5.39e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.27
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:39.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5055.26
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.79
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.74
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11508.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.68
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.58
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999935156

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.35
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000030445

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :  -0.062
p-value of test                       :    0.52

Sample variance                       :    0.17
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:02.48

 All tests were passed




Server wird beendet - Lösche Semaphor 115081231.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5505
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7141
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:04.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:55.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:00.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    2.44
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:11.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    3.59
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:41.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.84
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.93
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.64
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.75
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.38
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:44.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1409.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:02.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6920.73
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.35
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:06.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.45
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.12
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:33.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5183.38
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:54.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45390
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869390
  j =  1                              :        399909224
  j =  2                              :            45382
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45686
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869686
  j =  1                              :        399908629
  j =  2                              :            45684
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:27.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 3.06e-4
p-value of test                       :    0.9997    *****

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:17.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 3.76e-4
p-value of test                       :  3.5e-3

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.041
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:37.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.52
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.51
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.94
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.45
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:39.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.26
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.05
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17208.50
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.97
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.61
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.54
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.69
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.67
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.39
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.32
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.14
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.33
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.15
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.00
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.25
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.56
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.29
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.76
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.74
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.12
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.66
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.41
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.46
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.92
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.86
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.91
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  157.54
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.88
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.87
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5164.55
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.61
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  160.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.05
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :    1.64
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:24.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.86
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    1.41
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:23.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 2.96e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.08
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.53
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.34
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:04.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.60
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:04.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9855.98
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10165.26
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:47.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.31
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4778.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:49.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.06
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.64
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11701.01
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11761.19
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.58
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000111520

Normal statistic for number of bits   :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.97
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999924938

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.81
p-value of test                       :    0.04

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:33.59

 All tests were passed




Server wird beendet - Lösche Semaphor 116031503.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5214
p-value of test                       :    0.9976


-----------------------------------------------
CPU time used                    :  00:03:56.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:58.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:06.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:05.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:55.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7482
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:00.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.68
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9915

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.94
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.42
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:13.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    2.15
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.52
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.02
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.29
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.46
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.29
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.29
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.88
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.15
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:00.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7194.30
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.59
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.42
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.72
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.45
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.61
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5047.94
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:54.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908480
  j =  2                              :            45751
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45750
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869750
  j =  1                              :        399908503
  j =  2                              :            45744
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:27.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.11e-3
p-value of test                       :    0.9927

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:18.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:35.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.68e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.052
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:38.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.55
p-value of test                       :  5.4e-3

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.89
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:47.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.28
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.95
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.62
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.15
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:39.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.74
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.41
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.47
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.18
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17281.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.04
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.22
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.66
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.27
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.66
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.75
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.10
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.87
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.37
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.20
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.72
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.67
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.96
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.49
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.60
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.31
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.03
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.69
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.30
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.91
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.71
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.99
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4878.37
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.41
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  154.65
p-value of test                       :    0.9925


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.90
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.79
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.61
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  440.78
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.37
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.23
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.37
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:23.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.48e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 3.81e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 5.73e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.80
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.82
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:05.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.22
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:05.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.61
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9791.04
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.015
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:43.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4734.96
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4741.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.07
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.57
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11855.23
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11768.76
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.04
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999855875

Normal statistic for number of bits   :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.71
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000102109

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.69
p-value of test                       :    0.95

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:27.95

 All tests were passed




Server wird beendet - Lösche Semaphor 117047311.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:59.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:58.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5477
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:55.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4202
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:58.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:06.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7472
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:06.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7063
p-value of test                       :    0.9986


-----------------------------------------------
CPU time used                    :  00:03:54.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:00.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.36
p-value of test                       :  5.9e-3

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:12.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    3.10
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:43.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.76
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.72
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.79
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.19
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.53
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.08
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  272.40
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.53
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6972.96
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:42.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.82
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.18
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:06.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.91
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.26
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:33.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5188.73
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:57.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46125
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870125
  j =  1                              :        399907752
  j =  2                              :            46121
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45817
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869817
  j =  1                              :        399908368
  j =  2                              :            45813
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-3
p-value of test                       :    0.9982

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:28.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:18.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:01.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:55.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.54e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.06e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:35.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.34
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.35
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.88
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.59
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:36.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.91
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.37
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17715.05
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.00
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.57
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.73
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.11
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.96
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.47
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.79
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.84
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.20
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.55
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.02
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.19
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.46
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.69
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.72
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  197.64
p-value of test                       :  2.9e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.29
p-value of test                       :  9.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.89
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.60
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.43
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.43
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.44
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.96
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.62
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.95
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.00
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.92
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.91
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.84
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.16
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.46
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.37
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:25.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 2.76e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.43
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.95
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.20e-3
p-value of test                       :    0.9946

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.92
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:06.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.95
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:06.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10288.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:45.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.26
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:47.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.28
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.79
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.56
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12022.11
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.77
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.29
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999889214

Normal statistic for number of bits   :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.23
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999950189

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:52.45

 All tests were passed




Server wird beendet - Lösche Semaphor 118063119.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5516
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:00.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:46.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:02.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:10.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:13.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    2.40
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     961
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.44
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:14.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.67
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.98
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.75
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.28
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.91
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.53
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.92
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.85
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:57.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:08.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6952.29
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:59.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.10
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:21.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.30
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:47.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.52
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5041.47
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:59.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45891
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869891
  j =  1                              :        399908223
  j =  2                              :            45881
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45752
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869752
  j =  1                              :        399908502
  j =  2                              :            45740
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:33.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:20.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:54.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:10.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:01:39.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.15e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:52.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:52.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.81
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.23
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.51
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.54
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   48.53
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.90
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.70
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17293.72
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.56
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.86
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.01
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.28
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.34
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.19
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.99
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.13
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.08
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.50
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.38
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.26
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.47
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.55
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.24
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.52
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.20
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.05
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.83
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  308.75
p-value of test                       :    0.9981


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.76
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.56
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.24
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.68
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.68
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.73
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.04
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.01
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.95
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :   -1.59
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:24.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.44
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 3.98e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.61e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 6.30e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.21
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.85
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.46
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:04.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.90
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:05.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9956.88
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.21
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.17
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:04:30.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:55.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4655.65
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3979.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11966.71
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:35.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.13
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.99
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999965822

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.51
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000038473

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   0.068
p-value of test                       :    0.47

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.23
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:12.19

 All tests were passed




Server wird beendet - Lösche Semaphor 119078927.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:50.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:57.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:41.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:57.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:05.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7097
p-value of test                       :    0.9952


-----------------------------------------------
CPU time used                    :  00:03:05.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:59.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:01.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.92
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     959
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.24
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:16.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    3.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:44.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.16
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.58
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.21
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.38
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.84
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.22
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6972.55
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.64
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.37
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:03.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.02
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.07
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5004.08
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:59.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45845
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869845
  j =  1                              :        399908313
  j =  2                              :            45839
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45821
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869821
  j =  1                              :        399908361
  j =  2                              :            45815
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:28.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:17.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:01.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:56.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:32.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.37e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.76e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.24e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:40.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.26
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:48.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.99
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.59
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.52
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17524.72
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.44
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.33
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.87
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.00
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.04
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.90
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.25
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.66
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.88
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.04
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.93
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.76
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.04
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.70
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.00
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.37
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.07
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.73
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.27
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.00
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.63
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4873.51
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.28
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.28
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.06
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.64
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5155.03
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.64
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.03
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.32
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :   0.048
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.56
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    1.40
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:24.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.28e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 6.57e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.56e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.71
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.69
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.17
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:05.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.13
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:05.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10151.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.23
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:42.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:50.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:51.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.78
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.18
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.78
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.72
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999843227

Normal statistic for number of bits   :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.68
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999911117

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.19
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:27.40

 All tests were passed




Server wird beendet - Lösche Semaphor 120324111.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:39.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:57.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4457
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:59.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:07.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:07.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:00.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:05.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    3.18
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     957
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.93
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:15.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:44.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.07
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.47
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.23
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.95
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.01
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.23
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6813.88
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.64
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:08.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.19
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.71
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.21
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:59.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45732
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869732
  j =  1                              :        399908544
  j =  2                              :            45716
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46016
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870016
  j =  1                              :        399907970
  j =  2                              :            46012
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9916


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:29.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:18.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:02.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:36.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.35e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.78e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.72
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.01
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.95
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.05
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.81
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9916

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.85
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17225.02
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.49
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.47
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.95
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.91
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.73
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.00
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.70
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.57
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.49
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.63
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.15
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.89
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.76
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.20
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.11
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.10
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.95
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.90
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.30
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.73
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5167.86
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.74
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.19
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:34.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.57
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.18
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.20
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.45
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.47
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:33.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.05
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -2.13
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:17.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.39
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:18.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.58e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.06
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.44
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  1.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    5.25
p-value of test                       :  2.3e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  148.70
p-value of test                       :    0.9974

-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:59.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.55
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10142.62
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:30.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.82
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.23
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:46.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.24
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11528.01
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.95
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999963188

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.84
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000094216

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:58.20

 All tests were passed




Server wird beendet - Lösche Semaphor 121339919.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:48.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1264
p-value of test                       :    0.9968

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334384
  j =  1                              :        599997472
  j =  2                              :             1264
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:45.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:38.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:38.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:58.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7485
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:07.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:08.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:05.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:10.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:14.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.48
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:46.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.36
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.19
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.57
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.40
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.52
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:58.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.39
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:10.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6938.12
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:12.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.59
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.25
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:40.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5201.70
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:02.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45783
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869783
  j =  1                              :        399908435
  j =  2                              :            45781
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45781
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869781
  j =  1                              :        399908439
  j =  2                              :            45779
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:27.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:19.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:09.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9943

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:39.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.35e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:54.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:55.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.02
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.56
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.01
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.25
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.17
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17219.73
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.67
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.51
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.09
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.73
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.72
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.13
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.70
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.12
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.98
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.80
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.93
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.24
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.59
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.16
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.57
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.61
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.86
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.56
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.46
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.52
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.35
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.70
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.63
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.72
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4919.56
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.04
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.86
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.31
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.35
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    1.34
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:25.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 3.08e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.57
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.12
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.23
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:28.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:28.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9964.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:10.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:04:38.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:54.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    5.15
p-value of test                       :  2.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4602.01
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:01:58.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3965.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.21
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11926.13
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:29.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.75
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:31.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.07
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000020665

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.13
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999756353

Normal statistic for number of bits   :   -1.93
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
p-value of test                       :    0.9998    *****

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.62
p-value of test                       :    0.9957

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:21:00.71

 All tests were passed




Server wird beendet - Lösche Semaphor 102105104.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5533
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:50.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4450
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:37.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:54.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:06.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:04.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:58.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:00.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:12.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.99
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.46
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.23
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.34
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.25
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  262.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1361.99
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:02.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7013.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:44.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.03
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:04.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.56
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.08
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5109.63
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:51.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45766
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869766
  j =  1                              :        399908472
  j =  2                              :            45758
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45903
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869903
  j =  1                              :        399908195
  j =  2                              :            45901
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:25.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:17.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:45.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 7.78e-3
p-value of test                       :    0.9910

Anderson-Darling statistic = A2       :    3.65
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9969


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:01.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:39.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   97.34
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.94
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.31
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.66
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.21
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.82
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:40.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.65
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.19
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.13
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17246.39
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.30
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.90
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.14
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.25
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.36
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.30
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.93
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.70
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.13
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.21
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.05
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.50
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.84
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.24
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.07
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.83
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.67
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.51
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.82
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.14
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5168.59
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.72
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.75
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.92
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.34
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.06
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.20
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.65
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.04
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   0.097
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:24.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.96
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    1.48
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.01e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.24e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.32
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.78
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.63
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:06.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10058.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9818.14
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.027
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:42.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4981.80
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:48.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.42
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.22
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11982.34
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11983.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.89
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999977198

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.29
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999988148

Normal statistic for number of bits   :  -0.094
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.78
p-value of test                       :    0.04

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:22.14

 All tests were passed




Server wird beendet - Lösche Semaphor 103579664.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1265
p-value of test                       :    0.9966

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334385
  j =  1                              :        599997470
  j =  2                              :             1265
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5399
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:49.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:38.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:38.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:54.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:05.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:55.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:00.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:11.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    2.10
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     177
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:30.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.37
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.75
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.18
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.31
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.74
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.95
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:45.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:01.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6968.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:44.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.88
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:04.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.01
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.49
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:33.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5226.43
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:52.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45702
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869702
  j =  1                              :        399908600
  j =  2                              :            45694
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45795
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869795
  j =  1                              :        399908417
  j =  2                              :            45781
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:26.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:18.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:01.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:54.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:32.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 3.02e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.27e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.048
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:38.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:38.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.20
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.03
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.83
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.83
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.53
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 3.06e-3
p-value of test                       :    0.9969

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17773.87
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.39
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.12
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.24
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.78
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.59
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.55
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.40
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.95
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.02
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.83
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.02
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.40
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  182.75
p-value of test                       :  4.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.41
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.45
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.90
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.41
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.15
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.05
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4844.87
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.84
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  241.28
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.74
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.37
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.96
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.29
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.40
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.64
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:24.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.11
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:24.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 6.10e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.93e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.71
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.40
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:07.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.11
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:07.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9870.53
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.61
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:47.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4991.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4767.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:50.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.63
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4198.00
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11562.83
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11954.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.62
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999980219

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.86
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000035950

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.05
p-value of test                       :    0.98

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    2.79
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:35.45

 All tests were passed




Server wird beendet - Lösche Semaphor 104497168.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5568
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:48.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:38.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:37.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:53.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:55.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:05.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:05.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:59.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:59.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    2.07
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.68
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    2.24
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:12.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:40.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.85
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.08
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.38
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.39
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7116.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.39
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 9.62e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.58
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:35.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.25
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:53.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45709
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869709
  j =  1                              :        399908591
  j =  2                              :            45691
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45891
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869891
  j =  1                              :        399908221
  j =  2                              :            45885
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:27.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:20.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.98e-3
p-value of test                       :    0.9957

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:54.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.84e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:43.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.92
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.66
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.40
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.81
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.30
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.30
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.98
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17563.96
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.30
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.63
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.24
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.68
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.46
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.98
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.00
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.22
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.61
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.96
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.28
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.49
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.25
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.04
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.57
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.73
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.21
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.64
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.82
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.47
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.34
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.30
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.48
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.60
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.30
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4938.52
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.38
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.86
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.64
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :  -0.060
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:24.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.72
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:24.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.01e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.89e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.50
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.85
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.81
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.82
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:06.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10064.80
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.39
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.075
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:04:04.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.04
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5002.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4304.83
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4051.82
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11685.97
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11606.99
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:29.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.61
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999870848

Normal statistic for number of bits   :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.96
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000036355

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    2.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.13
p-value of test                       :    0.98

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:09.53

 All tests were passed




Server wird beendet - Lösche Semaphor 105447440.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1488
p-value of test                       :  5.0e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334608
  j =  1                              :        599997024
  j =  2                              :             1488
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5342
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:49.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:37.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:36.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:04.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:05.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:01.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.48
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:11.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.32
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    2.11
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.14
p-value of test                       :    0.9990

-----------------------------------------------
CPU time used                    :  00:02:41.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.01
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.53
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.11
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.39
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.09
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.31
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7194.28
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.94
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:04.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.50
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.33
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:32.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5076.59
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:58.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46101
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870101
  j =  1                              :        399907800
  j =  2                              :            46097
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46016
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870016
  j =  1                              :        399907971
  j =  2                              :            46010
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:27.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:18.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:53.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:33.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.04e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:38.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.41
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.06
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.11
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.84
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.34
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.69
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.39
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:38.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.38
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.097
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17367.40
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.12
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.51
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.60
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.83
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.96
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.84
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.87
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.43
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.18
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.81
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.74
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.42
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.60
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.17
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.48
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.23
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.01
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.95
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.75
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.80
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.24
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.78
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.32
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.06
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.16
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.34
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5171.21
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.75
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.16
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.01
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -1.38
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.81
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:24.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.19
p-value of test                       :    0.99

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 3.77e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.09
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.05
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.55
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.83
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:07.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10060.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10067.78
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:42.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.67
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.89
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.88
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4008.27
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11965.37
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11811.93
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.83
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999964532

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.26
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000021607

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:37.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           5.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 106463248.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5374
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:49.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:38.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:36.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7061
p-value of test                       :    0.9987


-----------------------------------------------
CPU time used                    :  00:03:06.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:59.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:03.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:12.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:43.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.83
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.44
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.08
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.50
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.74
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.88
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:53.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.11
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7054.71
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.59
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.70
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.00
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.07
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.96
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:38.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4957.14
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:54.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46234
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870234
  j =  1                              :        399907536
  j =  2                              :            46226
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45846
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869846
  j =  1                              :        399908313
  j =  2                              :            45836
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:28.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:18.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:03.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 5.42e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.20
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:45.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.63
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.26
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.30
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.70
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.89
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.02
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17168.25
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.82
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.24
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.36
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.74
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.10
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.14
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.04
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.75
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.38
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.54
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.70
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.47
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.89
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.92
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.11
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.50
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.61
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.83
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.82
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5105.29
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.51
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.85
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.85
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.72
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5094.44
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.56
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.14
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.51
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:23.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.62
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:24.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.88e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.99e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 2.93e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.26
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.17
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:07.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.77
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10113.40
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.18
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:04:18.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.83
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:56.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.14
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:56.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11707.12
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:31.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11811.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:31.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.44
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999938384

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.96
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000033964

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    2.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:21.94

 All tests were passed




Server wird beendet - Lösche Semaphor 107413520.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:51.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1488
p-value of test                       :  5.0e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334608
  j =  1                              :        599997024
  j =  2                              :             1488
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5457
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:52.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:04.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:01.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:13.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     126
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:43.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.18
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.66
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.68
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.40
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.03
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.15
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.53
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.35
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  488.13
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6994.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.58
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.51
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:03.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.12
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.38
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5143.37
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:56.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45870
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869870
  j =  1                              :        399908261
  j =  2                              :            45868
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45658
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869658
  j =  1                              :        399908687
  j =  2                              :            45652
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:26.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  5.4e-3

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:16.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:44.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:59.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.068
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:38.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.54
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.42
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.38
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.82
p-value of test                       :  8.1e-3

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   51.55
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.66
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.62
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.78
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17273.59
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.41
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.89
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.58
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.75
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.29
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.80
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.49
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.22
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.75
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.47
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.30
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  433.20
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.32
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.20
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.42
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.83
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.48
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.57
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.80
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.25
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.35
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5052.03
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.24
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  162.88
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.82
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.14
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4832.01
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.10
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.34
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.29
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -1.50
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:24.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.96
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:26.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.63
p-value of test                       :    0.05

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 6.45e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.95
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.75
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.61
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:05.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.75
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:05.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.55
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10046.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.30
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:40.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.61
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.69
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.24
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12098.19
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11793.45
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.41
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000085363

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.17
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000046402

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:46.52
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           5.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 108527632.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5522
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:52.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7149
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:03.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:04.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7488
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:01.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.98
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.26
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:13.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.70
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:42.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.65
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.15
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.78
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.14
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.78
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.45
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1546.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7070.12
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:41.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.06
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:02.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.83
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.43
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:34.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4967.55
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:53.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45951
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869951
  j =  1                              :        399908099
  j =  2                              :            45949
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46001
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870001
  j =  1                              :        399908005
  j =  2                              :            45987
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:25.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:16.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:54.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 5.98e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.75e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.80e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:33.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.97
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  101.74
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.39
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.58
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.57
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.71
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.26
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17064.26
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.20
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.69
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.53
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.03
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.41
p-value of test                       :    0.9944


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.48
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.44
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.62
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.15
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.38
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.30
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.68
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.25
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.68
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.55
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  429.53
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.79
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.45
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.11
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.14
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.36
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.76
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.11
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.11
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5135.51
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  430.26
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.59
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.09
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -1.55
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:22.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.67
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:24.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.20
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.22
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.29
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-3
p-value of test                       :    0.9988

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  249.81
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9849.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:42.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.84
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4731.84
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:50.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.30
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.84
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11962.66
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11840.60
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.47
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000058441

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.44
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000038959

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:45.37

 All tests were passed




Server wird beendet - Lösche Semaphor 109477904.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5455
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:51.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:39.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4223
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:04.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:55.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:00.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    3.76
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9943

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:11.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.40
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.66
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.23
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.99
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.74
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.15
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.24
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.42
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  367.61
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:01:43.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.89
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:00.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7216.47
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.86
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.88
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:03.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.42
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.84
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.24
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:58.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46423
p-value of test                       :  5.7e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870423
  j =  1                              :        399907158
  j =  2                              :            46415
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45755
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869755
  j =  1                              :        399908492
  j =  2                              :            45751
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:27.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:17.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:01.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:37.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   34.32
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.19
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.02
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.45
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.18
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.72
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.77
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.62
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.48
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17283.84
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.49
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.03
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.14
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.87
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.23
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.31
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.82
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.85
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.05
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.21
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.13
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.23
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.72
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.66
p-value of test                       :  6.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.07
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.23
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.20
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.16
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.48
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.92
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.90
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.62
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.83
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.89
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4787.47
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.10
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.34
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.71
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:23.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.02
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:23.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 7.62e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.98e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.89
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.78
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:06.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:08.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.95
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:39.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4985.65
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.49
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3895.82
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11977.81
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.60
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000056803

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.03
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999902462

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:02.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 59  WeightDistrib, r = 0            0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 110428176.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1252
p-value of test                       :    0.9989

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334372
  j =  1                              :        599997496
  j =  2                              :             1252
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5549
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:54.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:42.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7161
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:11.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:10.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:09.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:13.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    2.16
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:13.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.27
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:40.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.15
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.95
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.20
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.55
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   28.34
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.71
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  262.08
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  392.56
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:59.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.94
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:05.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6948.40
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.57
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:15.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.72
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.69
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4929.97
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:58.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46108
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870108
  j =  1                              :        399907787
  j =  2                              :            46102
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45931
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869931
  j =  1                              :        399908141
  j =  2                              :            45925
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:32.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:22.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:13.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.18e-3
p-value of test                       :    0.9988

Anderson-Darling statistic = A2       :    5.54
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.45e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 2.82e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:52.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.16
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.46
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.84
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.28
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.28
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.11
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:51.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.85
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.20
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.34
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17373.21
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.75
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.58
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.82
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.96
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.47
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.60
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.93
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.74
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.46
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.05
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.03
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.74
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.97
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.34
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.58
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.18
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.97
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.16
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.00
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.37
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.07
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.95
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.35
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.96
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4830.87
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.30
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.08
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.82
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :   -2.09
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:24.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.90
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:24.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    2.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.40e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.72e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.40
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.22
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.50
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.65
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:05.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9710.45
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10088.86
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : -7.24e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:04:31.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.94
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:56.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4750.74
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:59.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3979.71
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11777.56
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:38.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11768.24
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.46
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999906464

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.89
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000056377

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.96

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:25.85

 All tests were passed




Server wird beendet - Lösche Semaphor 111312912.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5482
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:53.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4452
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7468
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:04.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:54.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:00.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:13.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    2.91
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.68
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   37.53
p-value of test                       :  4.5e-3

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.30
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.38
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.23
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.84
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.09
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.10
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:43.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:01.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7085.64
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.13
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:04.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.45
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.61
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:33.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5099.54
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:56.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46051
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870051
  j =  1                              :        399907900
  j =  2                              :            46047
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45915
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869915
  j =  1                              :        399908175
  j =  2                              :            45905
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:27.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:19.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.58e-3
p-value of test                       :    0.9913

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:34.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.36e-6
p-value of test                       : 1 -  7.4e-5    *****

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.35
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.040
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.29
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:48.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.54
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.52
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.56
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.13
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.42
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:43.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.53
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.23
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.05
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17686.19
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.77
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.24
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.51
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.74
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.02
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.11
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.97
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.46
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.60
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.12
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.97
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.75
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.85
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.78
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.99
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.94
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.32
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.35
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.14
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.88
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.60
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.94
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.33
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.97
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.67
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.90
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.21
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.34
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.11
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:25.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.78
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -1.49e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:24.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.11e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.21e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.88
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.23
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.48
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:05.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:05.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.11
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10090.79
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.036
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:43.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4647.47
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.85
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.21
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.11
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11631.51
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.97
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999867611

Normal statistic for number of bits   :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.76
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999939614

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.2e-3

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:39.27

 All tests were passed




Server wird beendet - Lösche Semaphor 112492560.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5431
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:53.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:39.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:06.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:56.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7469
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:02.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.27
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    2.23
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     845
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.86
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:45.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.35
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:13.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.82
p-value of test                       :  3.9e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:43.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.94
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.67
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.54
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.68
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.61
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.79
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.24
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:59.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6879.81
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:39.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.37
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:06.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   16.40
p-value of test                       :  5.8e-3


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.05
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:31.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5184.54
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:57.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45765
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869765
  j =  1                              :        399908473
  j =  2                              :            45759
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45488
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869488
  j =  1                              :        399909025
  j =  2                              :            45486
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:27.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:19.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:02.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.26e-6
p-value of test                       :    0.9984

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 7.80e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.89
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:34.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:35.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.26
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.87
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.14
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.39
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.67
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:38.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.04
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.05
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.81
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17452.87
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.82
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.92
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.43
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.48
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.61
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.29
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.13
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.89
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.27
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.96
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.36
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.11
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.11
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.17
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.20
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.03
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.69
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.97
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.98
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.45
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.60
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.71
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4818.67
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.48
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.58
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.28
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.36
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5139.58
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.55
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.39
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.02
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:24.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.24
p-value of test                       :  9.9e-3


-----------------------------------------------
Normal statistic for number of jumps  :   -2.07
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:24.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.66e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 7.96e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.31e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.82
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.85
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.40
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:05.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.13
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:04.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.31
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10169.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.097
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:39.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4782.20
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4768.60
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4046.54
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.57
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11574.57
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.20
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000072343

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.94
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999777737

Normal statistic for number of bits   :   -1.76
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    2.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:05.57

 All tests were passed




Server wird beendet - Lösche Semaphor 113475600.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5357
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:52.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4212
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:38.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:55.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4225
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:03.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:03.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:54.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:59.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.27
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:15.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.46
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.07
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.36
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.13
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:43.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.15
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:01.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7040.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.16
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:17.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.50
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  150.91
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:36.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5040.77
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:58.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45418
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869418
  j =  1                              :        399909167
  j =  2                              :            45412
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46176
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870176
  j =  1                              :        399907651
  j =  2                              :            46170
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  9.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:28.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:19.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:59.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:55.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:34.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.44e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.57e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:38.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:37.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.86
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.30
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.02
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.86
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.75
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.28
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.29
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.29
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17388.02
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:54.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.63
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.59
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.39
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.98
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.89
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.21
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.00
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.26
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.86
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.31
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.77
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.65
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.14
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.88
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.21
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.72
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.36
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.90
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.71
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.16
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.57
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.51
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4845.56
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.66
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.50
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.45
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.01
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.18
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.26
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.25
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:23.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.76
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :  -0.028
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:23.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.27e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.92
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.70
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  252.70
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:02:03.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.92
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:04.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9887.12
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : -2.45e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:47.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.31e-3
p-value of test                       :    0.9955

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5126.51
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4728.48
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:51.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.66
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.14
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11861.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11814.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   99.20
p-value of test                       :  1.7e-4    *****


-----------------------------------------------
Total number of bits:  8000122215

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.54
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000102625

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.5e-3

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.31
p-value of test                       :    0.01

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:37.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 101  Run of bits, r = 0              1.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 114425872.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5344
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:53.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:38.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:02.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:03.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:54.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:00.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    2.10
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9941


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.29
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.91
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     263
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:16.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    2.01
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:42.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.62
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.65
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.15
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.93
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.49
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.04
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.92
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1406.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:01.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6942.91
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.41
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.31
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:03.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.62
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.61
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:32.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4971.33
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:57.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46072
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870072
  j =  1                              :        399907862
  j =  2                              :            46060
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45936
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869936
  j =  1                              :        399908130
  j =  2                              :            45932
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:19.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:45.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:58.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  2.4e-3

Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
p-value of test                       :    0.9917

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 7.52e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:36.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:36.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.56
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.74
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.11
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.30
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.82
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.08
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.41
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.30
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.39
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17717.09
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.24
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.81
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.22
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.34
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.10
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.72
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.24
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.12
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.50
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.96
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.24
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.15
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.45
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.49
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.77
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.33
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.96
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.87
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.88
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.89
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.48
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.39
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.95
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.60
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.46
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.98
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.06
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.70
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.03
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:23.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.65
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :   -1.78
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:22.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.74e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.59
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.55
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.41
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:03.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.98
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:05.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.41
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9766.39
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:43.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.23
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4785.73
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4013.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4198.30
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11678.64
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.83
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.17
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000074563

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   84.99
p-value of test                       :  4.5e-3


-----------------------------------------------
Total number of bits:  7999703913

Normal statistic for number of bits   :   -2.34
p-value of test                       :    0.9904



-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:57.06

 All tests were passed




Server wird beendet - Lösche Semaphor 115310608.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:57.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7470
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:40.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:04.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:55.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:02.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.14
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    4.57
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:02:14.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:43.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.10
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.80
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.48
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.27
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  191.57
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.69
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:51.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.98
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:02.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7240.37
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.28
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.60
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:03.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.90
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.69
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5085.37
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:57.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908198
  j =  2                              :            45901
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908069
  j =  2                              :            45961
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:17.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:44.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.7e-3

Kolmogorov-Smirnov- statistic = D-    : 4.67e-3
p-value of test                       :    0.9949

Anderson-Darling statistic = A2       :    3.91
p-value of test                       :  9.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9964


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:33.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.84e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.62e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:33.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.98
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.29
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.55
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.66
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.58
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:39.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.38
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.66
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17068.46
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.74
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.15
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.76
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.07
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.48
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.64
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.02
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.98
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.70
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.56
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.85
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.39
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.31
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.77
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.43
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.68
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.46
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.01
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.36
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.84
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.53
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.85
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.10
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.76
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.10
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.22
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.23
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4877.01
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.55
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.57
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.70
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    1.40
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:23.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.00
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  1.8e-3

Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
p-value of test                       :    0.9913

Anderson-Darling statistic = A2       :    5.02
p-value of test                       :  3.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -3.03
p-value of test                       :    0.9988

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 5.36e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.78
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.84
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:03.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9845.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.37
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.060
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:40.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 7.67e-3
p-value of test                       :    0.9918

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4698.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.21
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.41
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.79
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.75
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11919.27
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.69
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999936167

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.16
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000001546

Normal statistic for number of bits   :   0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.74
p-value of test                       :    0.04

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:46.22

 All tests were passed




Server wird beendet - Lösche Semaphor 116293648.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1221
p-value of test                       : 1 -  4.2e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334341
  j =  1                              :        599997558
  j =  2                              :             1221
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5272
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:56.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:05.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:54.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:00.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.67
p-value of test                       :  1.4e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    2.58
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:14.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:43.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.78
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.14
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.82
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.26
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.66
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.73
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:01.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7150.70
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:43.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.13
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.99e-3
p-value of test                       :    0.9969

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   92.53
p-value of test                       :  4.5e-3

-----------------------------------------------
CPU time used                    :  00:03:05.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.67
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   87.60
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:35.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4954.91
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:58.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45542
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869542
  j =  1                              :        399908920
  j =  2                              :            45534
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45682
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869682
  j =  1                              :        399908638
  j =  2                              :            45678
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:28.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:34.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.45e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.030
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:38.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.98
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.93
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.27
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   46.74
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.79
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.88
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.11
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17437.08
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.97
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.95
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.40
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.11
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.49
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.48
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.21
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.51
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.71
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.25
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.19
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.44
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.97
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.92
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.85
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.98
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.79
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.74
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.57
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.80
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.20
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.23
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.46
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.11
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.18
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.73
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.32
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.71
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.14
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.06
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :  -0.010
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.01
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.18
p-value of test                       :    0.99

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :  9.0e-3

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 4.27e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.23
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.53
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:04.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.83
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9712.67
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9724.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:39.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.93
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.22
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4016.84
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.97
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11908.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.72
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999914327

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.72
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000045277

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.08

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:16.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  8  CollisionOver, t = 7           1 -  4.2e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 117309456.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.91

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5332
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:59.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:42.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:00.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:11.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:11.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:05.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:09.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:03.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.09
p-value of test                       :  8.1e-3

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.86
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.15
p-value of test                       :    0.9983

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:15.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    2.07
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:43.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.69
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.24
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:11.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.02
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.43
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:54.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1487.05
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:07.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7105.47
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.01
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.18
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.02
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.86
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5084.48
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:56.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45813
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869813
  j =  1                              :        399908380
  j =  2                              :            45801
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45877
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869877
  j =  1                              :        399908247
  j =  2                              :            45875
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:36.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:27.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9971

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:15.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:38.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 8.61e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 8.66e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:43.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:44.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.23
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.18
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.21
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.95
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.12
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.92
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.83
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.76
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17223.44
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.15
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.96
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.48
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.32
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.96
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.69
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.83
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.54
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.26
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.05
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.02
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.66
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.79
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.87
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.81
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.65
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.40
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.68
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4866.73
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.14
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.96
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.42
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.50
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5088.59
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.83
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.36
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.03
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :   -1.00
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:22.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.07
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.94e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 5.74e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.74e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 6.25e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.35
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.66
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.77
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:04.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.38
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:03.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9702.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10195.31
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.072
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:04:34.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:55.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.47e-3
p-value of test                       :    0.9964

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5137.59
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:01:58.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.37
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4196.20
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12008.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:35.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:36.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.15
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999951368

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.74
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000042499

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:49.60

 All tests were passed




Server wird beendet - Lösche Semaphor 118325264.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:27.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5367
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:55.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:07.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:08.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:02.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:04.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     847
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:13.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.56
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.70
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.49
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.51
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.09
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.20
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.93
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.95
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:04.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6840.86
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-3
p-value of test                       :    0.9989

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   93.91
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:03:09.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.79
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.61
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5067.90
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:59.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45665
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869665
  j =  1                              :        399908675
  j =  2                              :            45655
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45963
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869963
  j =  1                              :        399908075
  j =  2                              :            45961
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:29.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:18.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  9.7e-3

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:46.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:02.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 8.68e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9917

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.20
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.33
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.07
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.17
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.24
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.23
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17189.76
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.07
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.45
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.49
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.39
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.94
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.92
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.28
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.19
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    4.80
p-value of test                       :    0.9983


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.39
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.68
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.47
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.50
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.44
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.99
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.95
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.56
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.04
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.49
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.57
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.96
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.64
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.83
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.80
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.28
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.36
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.70
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.21
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.48
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.71
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:20.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.68
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:20.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.44e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 5.74e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.33e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.74
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.07
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:04.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:05.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9840.90
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.6e-3

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10279.55
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:04:11.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4723.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:52.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.65
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:53.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.65
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11988.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11709.53
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:31.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.98
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999895589

Normal statistic for number of bits   :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.19
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000030907

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:18.12

 All tests were passed




Server wird beendet - Lösche Semaphor 119504912.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:27.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5331
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:54.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:41.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:59.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:07.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:08.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:59.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:00.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.16
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    2.21
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     648
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    2.57
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:12.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.18
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.75
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:11.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.95
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.90
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  473.92
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1552.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:03.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7217.85
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:06.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.62
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.95
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:36.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5058.94
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:59.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46295
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870295
  j =  1                              :        399907413
  j =  2                              :            46289
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46142
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870142
  j =  1                              :        399907718
  j =  2                              :            46138
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:29.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:18.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:45.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:01.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:02.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.77e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.93
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.14
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.28
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.61
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.20
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.35
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.46
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.91
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17226.28
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.72
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.45
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.31
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.04
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.42
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.40
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.84
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.89
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.40
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.31
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.17
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  422.13
p-value of test                       :    0.9951


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.16
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.06
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.76
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.58
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.82
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.16
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.32
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.96
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.07
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4832.79
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.59
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.17
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.91
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.97
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.57
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.02
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.71
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.82
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:21.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.12
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 2.45e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.06e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.10
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.22
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.17
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:04.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:04.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10124.83
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10178.41
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.088
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:04:01.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4744.03
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.95
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:51.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.18
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3956.40
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11781.92
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.14
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.26
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999972050

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.58
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000093388

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:42.73

 All tests were passed




Server wird beendet - Lösche Semaphor 120520720.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5570
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:55.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:56.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:57.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:05.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:05.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:55.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:00.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    3.06
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:12.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    2.30
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9925

-----------------------------------------------
CPU time used                    :  00:02:39.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.84
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.69
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.46
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.59
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.29
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  389.33
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:43.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1494.59
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6833.01
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.84
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.89
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:04.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.25
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.75
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:33.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4968.84
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:59.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45654
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869654
  j =  1                              :        399908696
  j =  2                              :            45646
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45784
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869784
  j =  1                              :        399908432
  j =  2                              :            45784
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:27.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:17.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.0e-3

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:58.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.92e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.70
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.81
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.87
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.70
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.64
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.08
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17143.19
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.32
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.53
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.68
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.22
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.83
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:34.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.71
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.62
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.22
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.27
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.67
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.84
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.41
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.07
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.41
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.21
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.26
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.19
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.10
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.90
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4887.98
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.11
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.40
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.38
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.48
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.86
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.67
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:14.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.28
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    1.64
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:14.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 7.83e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.35e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.50
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.80
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.57
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9931.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.19
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.76
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.33
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4253.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.16
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11862.77
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.41
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999892025

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.49
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999895688

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    1.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:57:06.30

 All tests were passed




Server wird beendet - Lösche Semaphor 121536528.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5411
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:44.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:37.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:34.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:05.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:05.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:02.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7460
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:03.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.25
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.01
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    3.81
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.48
p-value of test                       :  5.3e-3

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:09.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.98
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     127
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:42.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.66
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.32
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.54
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.64
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.91
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.93
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.11
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.69
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.27
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:02.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7040.40
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:43.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.65
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:03.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.23
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.19
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4813.86
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:05.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46091
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870091
  j =  1                              :        399907821
  j =  2                              :            46085
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45717
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869717
  j =  1                              :        399908569
  j =  2                              :            45711
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:29.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:19.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:01.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:52.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:33.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.83
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.68
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.45
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   48.78
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.30
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.17
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.88
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:29.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.46
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17566.79
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.17
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.68
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.66
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.35
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.59
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.84
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.42
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.11
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.11
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.43
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.79
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.63
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.83
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.07
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:47.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.65
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.89
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.80
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.29
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.99
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.26
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5139.53
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.19
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.38
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.84
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.18
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5141.60
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.13
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.21
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.18
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:20.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.43
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   0.079
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:16.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.74e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 9.17e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.41
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.36
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.87
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:08.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10044.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9900.73
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.62
p-value of test                       :  4.4e-3

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.099
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:46.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.81
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.93
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.22
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.46
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11683.12
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.45
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999965525

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.99
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999899921

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:14:04.37

 All tests were passed




Server wird beendet - Lösche Semaphor 102137873.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:50.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:44.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:36.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:34.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4582
p-value of test                       :  1.1e-4    *****


-----------------------------------------------
CPU time used                    :  00:01:53.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:54.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:00.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:01.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:53.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:09.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    2.18
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:39.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.40
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.54
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.20
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.16
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.65
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6969.80
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:43.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.39
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:03.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.22
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:47.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.59
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:34.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5162.33
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:02.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46166
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870166
  j =  1                              :        399907673
  j =  2                              :            46156
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46017
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870017
  j =  1                              :        399907970
  j =  2                              :            46009
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:29.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:18.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:53.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:32.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.59e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.58
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.55
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.11
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.54
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.62
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.09e-3
p-value of test                       :    0.9924

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.96
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.54
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.12
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.14e-3
p-value of test                       :    0.9957

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16973.70
p-value of test                       :    0.9931



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.41
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.26
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.52
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.76
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.97
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.16
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.88
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.01
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.13
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.75
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.26
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.24
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.84
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.69
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.17
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.60
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.13
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.35
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.03
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.99
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.56
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.64
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.20
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.64
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.22
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.13
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.31
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.23
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.85
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.86
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.38
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:18.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.15e-3
p-value of test                       :    0.9968

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.3e-3

Anderson-Darling statistic = A2       :    5.26
p-value of test                       :  2.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.12
p-value of test                       :  8.9e-4    *****

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 9.80e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.94e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 4.23e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.33
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.09
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.40
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:08.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.98
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10074.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.8e-3

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10310.52
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4784.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:49.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4801.30
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4018.96
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4303.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11956.88
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12068.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.27
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000045127

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.67
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999848237

Normal statistic for number of bits   :   -1.20
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   0.015
p-value of test                       :    0.49

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:47.23
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 16  BirthdaySpacings, t = 7         1.1e-4
 83  LempelZiv, r = 15               8.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 102924305.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5305
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:46.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:34.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:01.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:00.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7477
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:53.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:57.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.08
p-value of test                       :  8.3e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.36
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:11.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:39.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.00
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.14
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.17
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:44.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6840.99
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.45
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.12
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:03.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.70
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.63
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:32.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5005.69
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:01.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46139
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870139
  j =  1                              :        399907727
  j =  2                              :            46129
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45845
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869845
  j =  1                              :        399908312
  j =  2                              :            45841
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:28.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.98e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.095
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:32.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:32.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.07
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.60
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.28
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.87
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.18
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.86
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:40.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9947

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.41
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.12
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.57
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.16
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17359.06
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.45
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.09
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.61
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.05
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.51
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.11
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.90
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.90
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.06
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.61
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.12
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.85
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.08
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.61
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.52
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.74
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.77
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.89
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.89
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.09
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.06
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.67
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5082.61
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.68
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.93
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.48
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.05
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.71
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.99
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.15
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.13
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.22
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.65
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.04
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:05.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.74
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:07.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.72
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.95
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:50.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.52
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.05
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3978.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.55
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11690.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.69
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:29.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.48
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999972437

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.50
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000041653

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:18.31

 All tests were passed




Server wird beendet - Lösche Semaphor 103874577.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:39.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5479
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:50.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:38.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:35.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:54.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:01.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:01.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:52.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:56.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    2.84
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     943
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:10.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:38.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.71
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.02
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.07
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.53
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.42
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.83
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.14
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.47
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:00.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7125.03
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:41.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.84
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.88
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:03.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.33
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:46.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.85
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4965.35
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:56.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45957
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869957
  j =  1                              :        399908086
  j =  2                              :            45957
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45889
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869889
  j =  1                              :        399908223
  j =  2                              :            45887
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:28.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:18.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:44.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:59.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:55.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:32.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.15e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 9.77e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.014
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:34.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.53
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.71
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.50
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:47.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.88
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.57
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:38.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.86
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.50
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.06
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.13
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17474.15
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.47
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.45
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.30
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.28
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.26
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.02
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.95
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.53
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.73
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.87
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.17
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.38
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.09
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.94
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.04
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.09
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.57
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.12
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.92
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.13
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.86
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.92
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.02
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.43
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.87
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.21
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.96
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.30
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.64
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.66
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.16
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:22.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.06
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 7.25e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.75e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.39
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.75
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.62
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:05.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.70
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9878.89
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.069
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:51.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.85
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.01
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4339.68
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11655.93
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.20
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:29.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.56
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999922568

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.07
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999880952

Normal statistic for number of bits   :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :  -0.072
p-value of test                       :    0.53

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:28.30

 All tests were passed




Server wird beendet - Lösche Semaphor 104726545.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997115
  j =  2                              :             1441
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5348
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:54.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:40.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:37.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:54.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:54.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:01.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:01.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:53.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:58.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    2.48
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:11.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:38.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.23
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.65
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.57
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.27
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.59
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1382.01
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7011.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.37
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:03.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.35
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.63
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4976.57
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:54.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46157
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870157
  j =  1                              :        399907689
  j =  2                              :            46151
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45928
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869928
  j =  1                              :        399908148
  j =  2                              :            45920
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:28.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:17.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:43.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:59.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:55.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 7.29e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.95e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 9.30e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:33.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:34.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.46
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.62
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.83
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:47.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:37.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.06
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.38
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.79
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:39.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17359.77
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.94
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.26
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.88
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.35
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.70
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.20
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.46
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.97
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.67
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.06
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.20
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.56
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.07
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.97
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.39
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.52
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.20
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.98
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.84
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.64
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.94
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.55
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.41
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.64
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.64
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.36
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.24
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.73
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.39
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.02e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.45e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.05
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.63
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:05.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.10
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.07
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.86
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.60
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:55.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.59
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.71
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:51.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4246.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.67
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12108.44
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:30.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.61
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999920027

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.92
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000103726

Normal statistic for number of bits   :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    2.52
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:44.59

 All tests were passed




Server wird beendet - Lösche Semaphor 105709585.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5364
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:56.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:39.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:54.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:01.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:02.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:54.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:58.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.88
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    2.53
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.97
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    3.12
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     340
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:09.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.65
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:37.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.97
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.38
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.70
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.10
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.01
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.06
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.61
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.07
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.79
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6904.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.52
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.46
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:03.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.90
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4896.24
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:59.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46243
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870243
  j =  1                              :        399907516
  j =  2                              :            46239
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45743
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869743
  j =  1                              :        399908516
  j =  2                              :            45739
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:28.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:17.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:43.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:32.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.040
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.66
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.42
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:47.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.44
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.38
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.03
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    3.77
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   92.55
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17585.37
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.28
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.17
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.03
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.64
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.38
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.54
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.62
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.94
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.15
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.34
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.77
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.72
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.29
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.99
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.15
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.64
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.26
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.80
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.36
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.35
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.07
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.14
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.00
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.53
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.46
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.15
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.15
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.03
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:22.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.29
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    2.47
p-value of test                       :  6.7e-3



-----------------------------------------------
CPU time used                    :  00:02:20.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 5.23e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.96e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.71
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.82
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.72
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:07.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9825.01
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:44.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:49.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.68
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.17
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.93
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11693.16
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11690.39
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.67
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999943103

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.93
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999966062

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :  -0.079
p-value of test                       :    0.53

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:45.04

 All tests were passed




Server wird beendet - Lösche Semaphor 106725393.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1262
p-value of test                       :    0.9973

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334382
  j =  1                              :        599997476
  j =  2                              :             1262
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5572
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:57.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4453
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:02.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:02.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:54.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:58.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.83
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:14.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:44.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.13
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.57
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.57
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.95
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.70
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.24
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:44.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.19
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:02.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7187.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.06
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:04.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.54
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.56
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.78
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:53.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46023
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870023
  j =  1                              :        399907958
  j =  2                              :            46015
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46124
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870124
  j =  1                              :        399907759
  j =  2                              :            46110
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.95e-3
p-value of test                       :    0.9925

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:27.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.6e-3

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:59.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:33.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.48e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:38.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:38.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.03
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.17
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.21
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   13.84
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:01:40.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.67
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.92
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17463.53
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.45
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.32
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.27
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.31
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.90
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.57
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.48
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.51
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.10
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.93
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.56
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.11
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.05
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.50
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.63
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.89
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.15
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  304.39
p-value of test                       :    0.9989


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.31
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4772.91
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.75
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.47
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.02
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.81
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.53
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.37
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.38
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.47
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :  -0.033
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:22.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.52
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :   -1.76
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:21.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.30e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.83e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.86
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.80
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.36
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.33
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:06.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.49
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10024.11
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:43.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.73
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:49.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.99
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.98
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11977.61
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.22
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000041656

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.90
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999955391

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.44
p-value of test                       :    0.08

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:24.19

 All tests were passed




Server wird beendet - Lösche Semaphor 107773969.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:39.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:56.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7530
p-value of test                       :  7.0e-3


-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:03.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:03.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:53.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:59.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    3.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.33
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    2.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:15.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:43.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.36
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.89
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.71
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.62
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.58
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.40
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.06
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.23
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7071.81
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:42.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.46
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.85
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:03.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.34
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.98
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:33.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5177.06
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:58.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45938
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869938
  j =  1                              :        399908128
  j =  2                              :            45930
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46035
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870035
  j =  1                              :        399907933
  j =  2                              :            46029
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:28.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:19.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:59.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.10e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.30e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:40.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.47
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.51
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.69
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.11
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.92
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.33
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.62
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.72
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.72
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  160.30
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17658.01
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.41
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.95
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.03
p-value of test                       :    0.9928


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.17
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.62
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.88
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.99
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.06
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.22
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.14
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.77
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.79
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.65
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.67
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.38
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  432.90
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.42
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.97
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.45
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.19
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5120.58
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.16
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.79
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.40
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.11
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.41
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.27
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.79
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.40
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.96
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -1.53
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:22.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.24e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 6.61e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.77
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.05
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.61
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:04.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.80
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9983

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.12
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:38.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.95
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.1e-3

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5075.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4236.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.29
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.97
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.11
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:30.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.76
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999950408

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.22
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000032140

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.81
p-value of test                       :    0.04

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:00.67

 All tests were passed




Server wird beendet - Lösche Semaphor 108691473.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5480
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:59.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:43.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:58.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:05.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:03.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:53.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:59.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.96
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     954
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:15.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:45.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.25
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.43
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.06
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.47
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.15
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.73
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.98
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1370.26
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:04.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7245.35
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.98
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.32
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:05.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.18
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.41
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:33.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4777.04
p-value of test                       :    0.9960


-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:54.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46026
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870026
  j =  1                              :        399907951
  j =  2                              :            46020
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45781
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869781
  j =  1                              :        399908442
  j =  2                              :            45773
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:27.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:18.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:55.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:34.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.55e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.049
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:36.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.80
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:48.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.82
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.14
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.24
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   49.74
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:01:39.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.04
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.80
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.81
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.16
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17503.11
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.27
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.38
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.80
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.04
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.54
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.03
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.11
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.06
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.36
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.71
p-value of test                       :  6.8e-3


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.85
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.66
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.83
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.49
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.64
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.46
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.46
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.61
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.27
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.94
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.90
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.30
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5108.25
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.45
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.90
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.78
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.03
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.98
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.96
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.83
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.83
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:22.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.59
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:22.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 6.98e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.70e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 8.06e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.94
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.48
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.56
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:03.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.02
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:04.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9860.18
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:41.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.91
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4291.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12155.95
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11552.92
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:29.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.57
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999908078

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.78
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999815465

Normal statistic for number of bits   :   -1.46
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.84e-3
p-value of test                       :    0.9981

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    2.47
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:40.26

 All tests were passed




Server wird beendet - Lösche Semaphor 109707281.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5455
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:01.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7510
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:43.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:58.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:07.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:06.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:55.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:03.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     840
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9960


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:17.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:45.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.53
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.65
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.95
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.90
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.26
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.97
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.51
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.91
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.31
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7072.57
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:44.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.69
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.28
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:01.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.19
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.40
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:32.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5109.84
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:52.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45477
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869477
  j =  1                              :        399909048
  j =  2                              :            45473
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45811
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869811
  j =  1                              :        399908384
  j =  2                              :            45799
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:27.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:18.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:34.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:35.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.67
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.46
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.35
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:40.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.17
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.45
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17263.01
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.19
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.24
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.61
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.11
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.46
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.23
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.27
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.29
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.30
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.50
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.76
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.41
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.71
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.44
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.87
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.77
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.54
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.00
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.47
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.38
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.69
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.90
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.69
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.01
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.99
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.03
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.87
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.99
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:34.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.16
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:21.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.59
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:23.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.16e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 5.44e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.68e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 4.07e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.14
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.20
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:04.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:05.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9951.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9909.77
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.087
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:39.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:49.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4228.04
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.03
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.98
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12163.85
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   93.32
p-value of test                       :  7.2e-4    *****


-----------------------------------------------
Total number of bits:  7999965198

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.78
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999871643

Normal statistic for number of bits   :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    2.52
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.84
p-value of test                       :    0.97

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:25.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 101  Run of bits, r = 0              7.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 110723089.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5432
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:59.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:44.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4231
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:06.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7075
p-value of test                       :    0.9978


-----------------------------------------------
CPU time used                    :  00:03:06.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:55.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7514
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:04:00.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     649
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:13.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:41.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.18
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.10
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.68
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.35
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.42
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.28
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  499.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.16
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.62
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.94
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:32.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4981.55
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:00.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45830
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869830
  j =  1                              :        399908346
  j =  2                              :            45818
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46033
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870033
  j =  1                              :        399907936
  j =  2                              :            46029
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 8.84e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  3.4e-3

Anderson-Darling statistic = A2       :    5.54
p-value of test                       :  1.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  4.1e-4    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:25.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:17.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:34.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.83e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.022
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.27
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.70
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.71
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:47.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.10
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.51
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.69
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.33
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17535.81
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.05
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.38
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.06
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.02
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.63
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.64
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.31
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.93
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.52
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.14
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.32
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.64
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.50
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.08
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.59
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.69
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.95
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  437.79
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.45
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.91
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.59
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.31
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.50
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.44
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.55
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.79
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.35
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.07
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.09
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.87
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -1.26
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:22.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.74
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:22.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.73e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.94
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.07
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.88
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:03.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.9e-3

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.13
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:05.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9920

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10070.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:41.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.72
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.19
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:51.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4259.65
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.82
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11747.03
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11734.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:30.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.59
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999950048

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.22
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000055492

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.015
p-value of test                       :    0.51

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.43

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:20.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 46  MaxOft, t = 8                   4.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 111738897.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5387
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:58.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:43.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:57.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4472
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:06.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:06.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:55.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:14.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.54
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.38
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.08
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.63
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.47
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.53
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.49
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.54
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  388.25
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:49.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1487.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:05.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7074.13
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.65
p-value of test                       :  6.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.98
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:02.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.96
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.28
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:31.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4996.53
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:00.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45793
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869793
  j =  1                              :        399908415
  j =  2                              :            45791
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46150
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870150
  j =  1                              :        399907703
  j =  2                              :            46144
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:25.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:17.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:59.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.09e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.36e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:33.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.80
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   96.26
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.53
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.63
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.16
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.30
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17369.41
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.88
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.28
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.74
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.01
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.83
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.33
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.56
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.51
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.30
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.85
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.72
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.82
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.92
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.48
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.71
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.81
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.09
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.43
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.63
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  110.14
p-value of test                       :  4.1e-3


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.26
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.29
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.08
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.47
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.81
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.76
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.95
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5186.67
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.41
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.70
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.94
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :   -1.68
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:21.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.05
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    0.57
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:22.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 7.16e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.71e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.56e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.82
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.03
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.42
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:04.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.67
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:04.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10122.29
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:36.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.62
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5002.51
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.31
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11700.08
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11652.35
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.70
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999933404

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.02
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999994541

Normal statistic for number of bits   :  -0.043
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :  -0.060
p-value of test                       :    0.52

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:28.55

 All tests were passed




Server wird beendet - Lösche Semaphor 112754705.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5503
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:58.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:06.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:06.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:00.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.09
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    2.64
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:16.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    3.91
p-value of test                       :  9.7e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:43.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.14
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.79
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.04
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.55
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.07
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:44.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1374.54
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6927.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.74
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.36
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:03.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.80
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:32.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5000.66
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:00.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45490
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869490
  j =  1                              :        399909025
  j =  2                              :            45480
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45938
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869938
  j =  1                              :        399908127
  j =  2                              :            45932
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:25.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:18.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:59.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:53.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:32.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.16e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.57
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:35.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.44
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:47.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.05
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.49
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.00
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:37.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.47
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.28
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17381.15
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.46
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.85
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.22
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.88
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.58
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.31
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.43
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.98
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.25
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.82
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.71
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.59
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.58
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.65
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.79
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.22
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.37
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.77
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.66
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.47
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.14
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.71
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.43
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.95
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.20
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.05
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.33
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.96
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:34.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.13
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:22.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.07
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:23.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 7.45e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.16
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.60
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.04
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:03.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.69
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9815.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10140.13
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:55.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:39.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4694.89
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.53
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4008.76
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3985.90
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11642.60
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12057.40
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.70
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999976241

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.75
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999899735

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   0.094
p-value of test                       :    0.46

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:51.87

 All tests were passed




Server wird beendet - Lösche Semaphor 113770513.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1463
p-value of test                       :  4.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334583
  j =  1                              :        599997074
  j =  2                              :             1463
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1256
p-value of test                       :    0.9984

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334376
  j =  1                              :        599997488
  j =  2                              :             1256
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:00.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4195
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:43.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:46.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:02.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:09.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:08.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    2.10
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     852
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    5.77
p-value of test                       :  1.3e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     363
p-value of test                       :  2.3e-4    *****

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:13.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:43.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.66
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.84
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.59
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.12
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.20
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.06
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:51.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.41
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6945.81
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:51.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.79
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.65
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.17
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5210.59
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:02.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45899
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869899
  j =  1                              :        399908204
  j =  2                              :            45895
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45562
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869562
  j =  1                              :        399908883
  j =  2                              :            45548
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:29.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:16.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:38.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.94e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : -3.07e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:46.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.59
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.18
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.11
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.04
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:52.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.40
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.63
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17261.69
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.53
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.88
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.86
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.39
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.89
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.74
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.12
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.93
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.85
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.40
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.99
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  437.41
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.84
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.36
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.89
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.22
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.70
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.66
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.18
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.66
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.98
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.17
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  452.41
p-value of test                       :  9.2e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.18
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.58
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.86
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.27
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.33
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.18
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:21.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         : -5.43e-3
p-value of test                       :    0.50

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   0.060
p-value of test                       :    0.48

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.70
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.42
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:05.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.06
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:05.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10044.24
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.0e-3

Anderson-Darling statistic = A2       :    4.33
p-value of test                       :  6.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10358.18
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.082
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:04:25.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4779.39
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:55.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.5e-3

Kolmogorov-Smirnov- statistic = D-    : 9.78e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.06
p-value of test                       :  8.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4618.40
p-value of test                       :    0.9974

-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4209.06
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11537.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:34.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12109.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:34.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.02
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  7999972299

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.24
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999858539

Normal statistic for number of bits   :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:01.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs NJumps, t = 9        2.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 114786321.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5419
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:00.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7167
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:57.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:06.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:06.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:57.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:01.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:51.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.68
p-value of test                       :  1.4e-3

Test on the Nm values of W_{n,i}(mNP1):    2.11
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:18.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:49.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.49
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.53
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.63
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.94
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.54
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.20
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:44.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.19
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7146.11
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.62
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.76
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.64
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:32.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5076.72
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:04.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45705
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869705
  j =  1                              :        399908591
  j =  2                              :            45703
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46028
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870028
  j =  1                              :        399907948
  j =  2                              :            46020
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:27.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  7.6e-3

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:18.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:45.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:00.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:53.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 9.29e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:35.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.87
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:48.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.36
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.16
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.02
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.30
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17721.84
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.06
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.62
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.90
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.22
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.05
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.48
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.74
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.19
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.26
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.29
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.47
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.67
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.59
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.17
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.58
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.57
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.04
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.74
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.82
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.56
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.65
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.95
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4885.94
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.82
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.32
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.01
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.22
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.79
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.21
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.00
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.06
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.84
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :    1.92
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:23.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :  5.7e-3

Kolmogorov-Smirnov- statistic = D-    : 2.35e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.40e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.14
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.34
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:04.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:04.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9814.58
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10078.66
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:40.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.28
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4683.57
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:50.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.40
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4233.32
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.60
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11770.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.95
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000026344

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.02
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999898652

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.041
p-value of test                       :    0.52

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   0.078
p-value of test                       :    0.47

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:10.38

 All tests were passed




Server wird beendet - Lösche Semaphor 115900433.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:58.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:43.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:05.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:05.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:57.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:01.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.51
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     559
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:19.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    2.07
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:49.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.06
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.52
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.32
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.65
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:44.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1540.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:01.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7009.55
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.10
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:03.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.47
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.57
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.81
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:54.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45985
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869985
  j =  1                              :        399908035
  j =  2                              :            45975
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45926
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869926
  j =  1                              :        399908153
  j =  2                              :            45916
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:26.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:17.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:00.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:54.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:33.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-5
p-value of test                       :    0.9929

Kolmogorov-Smirnov- statistic = D-    : 2.70e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.72e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:34.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.89
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:47.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.87
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.58
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.24
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.25
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.86
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.67
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.70
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.71
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17477.70
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.83
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.82
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.68
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.94
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.92
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.23
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.37
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.39
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.56
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.38
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.28
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.32
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.10
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.56
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.86
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.46
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.30
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.48
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.02
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.33
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.74
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.01
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.95
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.23
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.53
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.15
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4861.24
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.72
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.83
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:34.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.53
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:21.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.12
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   -0.82
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:22.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.11e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.43e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.69e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.69
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.21
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:03.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.70
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:04.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.55
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.94
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.19
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:38.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.38
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.27
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:50.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.54
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4179.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11730.34
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11634.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.58
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999979379

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.25
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999956966

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    2.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:43.88

 All tests were passed




Server wird beendet - Lösche Semaphor 116916241.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:40.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:57.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:07.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:56.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:02.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:19.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    3.21
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:50.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.88
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.37
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.35
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.42
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.99
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.23
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1407.22
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7147.74
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:44.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:03.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.01
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.39
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5007.74
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46142
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870142
  j =  1                              :        399907724
  j =  2                              :            46126
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45582
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869582
  j =  1                              :        399908837
  j =  2                              :            45580
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:27.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:17.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:44.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:54.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.82e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.34e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:34.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:47.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.48
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.92
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.73
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:47.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.26
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.12
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:38.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.28
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.79
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17441.80
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.76
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.68
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.77
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.71
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.51
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.64
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.03
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.86
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.36
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.73
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.26
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.66
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.35
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.28
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.46
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.69
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.54
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.75
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.50
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.77
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.33
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4824.28
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.29
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.33
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.22
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.10
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5076.74
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.22
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.17
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:34.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.42
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -1.54
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:21.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.63
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    1.64
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.17

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 8.51e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 4.74e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.57
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.32
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:03.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10062.86
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9873.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:42.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5046.70
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.66
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11641.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.19
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999969350

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.03
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999909914

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:01.62

 All tests were passed




Server wird beendet - Lösche Semaphor 117899281.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5502
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4444
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4444
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7488
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:56.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:02.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    3.84
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:13.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.11
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:44.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.97
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.23
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.67
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.68
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.64
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.18
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.63
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.15
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:01.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7129.12
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:43.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.21
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.03
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:04.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.51
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.07
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4923.07
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  5.5e-3


-----------------------------------------------
CPU time used                    :  00:03:01.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46153
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870153
  j =  1                              :        399907697
  j =  2                              :            46147
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46252
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870252
  j =  1                              :        399907496
  j =  2                              :            46252
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:26.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:17.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:54.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.49e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.65e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:47.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.56
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.70
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.15
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.54
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.23
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.53
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.63
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:39.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17523.34
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.25
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.07
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.89
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.64
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.09
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.82
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.08
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.61
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.30
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.67
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.67
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.22
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.45
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.29
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.25
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.41
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.83
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.86
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.70
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.87
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.85
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.51
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5108.52
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.34
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.62
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.48
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.90
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4858.81
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.13
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.54
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.71
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:22.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.72
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.92
p-value of test                       :    0.03

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.80e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 7.89e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.55e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 4.02e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.14
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.99
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.04
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:03.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.13
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:04.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9971.87
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9903.30
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.089
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:55.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:40.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4780.08
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9948

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4204.83
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4224.33
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11656.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11895.60
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.26
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000026797

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.32
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000066238

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   0.100
p-value of test                       :    0.46

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:54.14

 All tests were passed




Server wird beendet - Lösche Semaphor 118915089.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5319
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:58.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:43.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:58.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:57.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:06.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:06.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:56.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:01.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:54.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:15.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:43.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.11
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.39
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.92
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.95
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.43
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.38
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.54
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.38
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.03
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.75
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:43.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.30
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7049.09
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:43.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.00
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.13
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:03.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.57
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.93
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:33.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5241.95
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:03.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45812
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869812
  j =  1                              :        399908379
  j =  2                              :            45806
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45935
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869935
  j =  1                              :        399908135
  j =  2                              :            45925
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:27.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:18.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:02.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.73e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:53.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:33.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.94
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.90
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.80
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.37
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.11
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.64
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.27
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.21
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.88
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.14
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17012.56
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.43
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.91
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.96
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.99
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.96
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.05
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.76
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.30
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.92
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.81
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.43
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.59
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.05
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.07
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.62
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.75
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.02
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.50
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.71
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.93
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.96
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.11
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.41
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.99
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.52
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.30
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.20
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.13
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:34.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.33
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -1.96
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.41
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   -2.00
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:21.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.087
p-value of test                       :    0.47

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.95e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 9.17e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.51
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.22
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.44
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:03.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:04.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9827.71
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10151.79
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.052
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:53.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4675.87
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.09
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.19
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11627.80
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12229.75
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.29
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000025981

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.57
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999938978

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:21.13

 All tests were passed




Server wird beendet - Lösche Semaphor 119930897.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5464
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:42.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:58.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:06.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:07.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:01.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    2.36
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     856
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:16.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.01
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    2.04
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:43.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.14
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.93
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.16
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.09
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.67
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:45.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1510.27
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6886.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.70
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:02.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.95
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5071.53
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:03.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45827
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869827
  j =  1                              :        399908348
  j =  2                              :            45823
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46297
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870297
  j =  1                              :        399907409
  j =  2                              :            46291
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:26.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:17.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:59.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:53.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:33.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.83e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.79e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 3.21e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:32.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:32.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.88
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.88
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.11
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.87
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.90
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.04
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.76e-3
p-value of test                       :    0.9982

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.87
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.04e-3
p-value of test                       :    0.9969

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  166.82
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17632.48
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.90
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.48
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.37
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.61
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.63
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.77
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.06
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.18
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.76
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.96
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.25
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.48
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.16
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.17
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.24
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.27
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.22
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.47
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.79
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.52
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.99
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4834.53
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.14
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.71
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.79
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.82
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5206.56
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.21
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.40
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.86
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:20.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.17
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:20.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 4.36e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.34
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.60
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.77
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:05.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:05.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9922.16
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10096.43
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:38.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.15e-3
p-value of test                       :    0.9946

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4678.95
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:47.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.27
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.16
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11594.03
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11637.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.93
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999951140

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.33
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999961412

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:32.04

 All tests were passed




Server wird beendet - Lösche Semaphor 120946705.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:42.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:35.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7144
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:33.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4459
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:54.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:00.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:00.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:52.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7505
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:58.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    3.25
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     972
p-value of test                       :  9.2e-3

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.56
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     261
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:13.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.02
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:35.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.73
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.92
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.60
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  281.85
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  384.95
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.61
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6979.79
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.21
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.88
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:03.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.87
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:35.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5049.90
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:03.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45660
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869660
  j =  1                              :        399908683
  j =  2                              :            45654
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45837
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869837
  j =  1                              :        399908330
  j =  2                              :            45829
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:30.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  7.9e-3

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  3.5e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:20.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:53.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.72e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 9.33e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.70e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:35.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.76
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:48.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.60
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.15
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:00:48.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.98
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.19
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:39.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.44
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.30
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.34
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.87
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17605.05
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.87
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.77
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.63
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.45
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.65
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.50
p-value of test                       :    0.9941


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.38
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.08
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.98
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.47
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.05
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.40
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.79
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.92
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:47.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.91
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.51
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  561.82
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.32
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  105.08
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.54
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.54
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.17
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.40
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.11
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.00
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.14
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.85
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.03
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.59
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.60
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:21.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.02
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:16.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.03
p-value of test                       :    0.98

Sample variance                       :    2.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 6.05e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.84e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.45
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.37
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.27
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:06.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.01
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:09.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10136.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9860.67
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:46.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.55
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:48.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.28
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:50.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.32
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11945.40
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12050.72
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:29.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.33
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999954848

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.70
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000094693

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
p-value of test                       :    0.9910

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.1e-3

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.26
p-value of test                       :    0.01

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:54.85

 All tests were passed




Server wird beendet - Lösche Semaphor 102170642.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5419
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:43.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4205
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:35.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4230
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:54.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:00.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:01.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:52.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:57.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:44.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:10.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:36.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.16
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.71
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.22
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  264.96
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.63
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.68
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6998.58
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.74
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.64
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:04.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.83
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:46.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.84
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:34.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4891.01
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:58.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45922
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869922
  j =  1                              :        399908163
  j =  2                              :            45908
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45667
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869667
  j =  1                              :        399908669
  j =  2                              :            45661
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:29.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:54.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:33.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.81e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.74e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.057
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -3.53
p-value of test                       :    0.9998    *****

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:34.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.08
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.76
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.33
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.89
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.43
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:39.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.56
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.17
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17468.33
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.08
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.55
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.03
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.66
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.49
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.04
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.30
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.81
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.19
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.82
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.66
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.27
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.85
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.87
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.96
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.95
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.00
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.08
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.79
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.74
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.78
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.01
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4849.23
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.05
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.02
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.58
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.33
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.03
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  430.77
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.83
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.34
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.18
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -1.15
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:19.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.83e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 8.43e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.84
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.24
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:08.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9917

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.41
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:08.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.93e-3
p-value of test                       :    0.9915

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9774.05
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10055.57
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:54.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.80
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.70
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:50.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4239.75
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.61
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.85
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000058684

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.29
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999944831

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.20

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:11.48
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 56  SampleCorr, k = 2               0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 102891538.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:04.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:05.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1471
p-value of test                       :  2.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334591
  j =  1                              :        599997058
  j =  2                              :             1471
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1470
p-value of test                       :  2.4e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334590
  j =  1                              :        599997060
  j =  2                              :             1470
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:47.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4217
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:37.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:37.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:05.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:06.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:03.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:03.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:12.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.73
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.15
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:11.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.34
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.76
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.84
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  381.10
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:07.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7202.07
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.06
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.54
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:17.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.35
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.35
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:41.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5172.02
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:56.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45897
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869897
  j =  1                              :        399908210
  j =  2                              :            45889
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46132
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870132
  j =  1                              :        399907738
  j =  2                              :            46128
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 9.46e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:32.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.95
p-value of test                       :  9.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:20.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:48.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:56.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:38.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.78e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 5.95e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : 9.52e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:24.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.78
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.25
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.65
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.63
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.26
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.63
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:51.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.20
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.16
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.46
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17676.07
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.72
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.84
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.45
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.44
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.92
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.82
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.20
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.02
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.81
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.15
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.61
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.20
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.21
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.54
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.82
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.96
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.69
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.77
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.71
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.44
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.50
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.86
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.87
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.10
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5090.05
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.81
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.90
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.66
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:24.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.33
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         : -5.43e-3
p-value of test                       :    0.50

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.53e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 8.16e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.10e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.11e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.26
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.40
p-value of test                       :    0.9942

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.25
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:08.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9971.99
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9892.66
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:04:28.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4756.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:55.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:59.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.73
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.34
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11985.12
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11733.92
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:38.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.05
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999990962

Normal statistic for number of bits   :  -0.071
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.54
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999898589

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.62
p-value of test                       :  4.4e-3

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.09
p-value of test                       :    0.02

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   0.056
p-value of test                       :    0.48

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:42.06

 All tests were passed




Server wird beendet - Lösche Semaphor 103743506.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:51.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:40.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:07.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:06.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:07.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:13.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.98
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:13.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:41.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.68
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.98
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.17
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.17
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.19
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:29.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.76
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1341.87
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:03.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7159.62
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.95
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.63
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:17.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.22
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.13
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4975.99
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:52.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45732
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869732
  j =  1                              :        399908540
  j =  2                              :            45724
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45855
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869855
  j =  1                              :        399908293
  j =  2                              :            45849
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:32.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:10.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:38.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 2.74e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 2.78e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.081
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.030
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.76
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.84
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.33
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.45
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:51.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.33
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.26
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17422.91
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.42
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.72
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.12
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.92
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.69
p-value of test                       :    0.9955


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.72
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.48
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.44
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.46
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.46
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.07
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  560.00
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.98
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.73
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.66
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.03
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.33
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.61
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.74
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.95
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.81
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.06
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.94
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.42
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.14
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.35
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5092.86
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.24
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.93
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.88
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.48
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:24.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 9.81e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.44
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.10
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :  9.4e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    5.45
p-value of test                       :  1.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  149.75
p-value of test                       :    0.9968

-----------------------------------------------
CPU time used                    :  00:02:06.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.35
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10060.65
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10169.94
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:11.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:04:27.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.71
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:57.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4716.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:59.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4376.80
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11989.71
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.70
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:37.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.78
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000146548

Normal statistic for number of bits   :    1.16
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.01
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999917996

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         : 4.40e-4
p-value of test                       :    0.50

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:24.39

 All tests were passed




Server wird beendet - Lösche Semaphor 105349138.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5336
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:47.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:05.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7532
p-value of test                       :  6.5e-3


-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:56.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:02.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    2.80
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:45.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:12.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.94
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     125
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:43.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.48
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.98
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.88
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.36
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.49
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.84
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1496.34
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6938.62
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:41.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.45
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.98
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.21
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5122.06
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:11.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869892
  j =  1                              :        399908220
  j =  2                              :            45884
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46024
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870024
  j =  1                              :        399907956
  j =  2                              :            46016
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:27.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:18.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:59.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:54.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:34.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 9.22e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.94
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.47
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.25
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.90
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.05
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.13
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.50
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9938

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.38
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17493.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.21
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.80
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.46
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.48
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.60
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.24
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.66
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.86
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.31
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.08
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.28
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.19
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  177.14
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.07
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.48
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.76
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.57
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.17
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.24
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.95
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.33
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.39
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.19
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.08
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.73
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.39
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.24
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.36
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.13
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   0.048
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:23.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.44e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 3.82e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.78
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.43
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.24
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:07.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.02
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:08.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10178.18
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10043.91
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.015
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:40.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.04
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4770.58
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.58
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.62
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11484.63
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.42
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999885419

Normal statistic for number of bits   :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.50
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000029905

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    2.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:23.95

 All tests were passed




Server wird beendet - Lösche Semaphor 106528786.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9904


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:47.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4233
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:38.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:39.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7484
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:04.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:53.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:59.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:13.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:42.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.66
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.96
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.05
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.95
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.26
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   27.11
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.84
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.16
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.32
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:44.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1375.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7113.05
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:45.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.42
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:05.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.17
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.98
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:34.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5205.42
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:09.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45937
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869937
  j =  1                              :        399908132
  j =  2                              :            45925
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46134
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870134
  j =  1                              :        399907733
  j =  2                              :            46132
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:25.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:17.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:01.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.57e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.048
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.08
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.84
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.87
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.66
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.25
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:42.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.17
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.85
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:36.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17320.25
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.49
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.05
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.48
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.78
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.87
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.19
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.91
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.01
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.22
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.99
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.10
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.60
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.52
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.84
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.47
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.68
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.52
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.72
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.93
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.16
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.58
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.23
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.66
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.69
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.57
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.05
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.31
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.10
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.49
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.48
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:23.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.98
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -1.47
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:24.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.43e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 9.40e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.74e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.28e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.94
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.77
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:07.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.58
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.071
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:43.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.21
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.16
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3952.41
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.22
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12017.34
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11907.88
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.57
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000089746

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.49
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999852599

Normal statistic for number of bits   :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:00.52
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 32  CouponCollector, r = 20         0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 107511826.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5283
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:48.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:40.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:08.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:01.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7491
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:04.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.40
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:13.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:44.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.86
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.02
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.71
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.34
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.88
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:52.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1484.54
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:02.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6981.83
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:57.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.92
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.52
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:14.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.56
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.15
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:38.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.93
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:02.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45984
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869984
  j =  1                              :        399908034
  j =  2                              :            45980
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45988
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869988
  j =  1                              :        399908029
  j =  2                              :            45978
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:29.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:17.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:06.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.68e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.92e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.069
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:52.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.43
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.39
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.00
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.88
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.93
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.40
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.40
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17665.40
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   58.20
p-value of test                       :  8.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.25
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.42
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.12
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.39
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.52
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.77
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.01
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.01
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.54
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.01
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.32
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.97
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.46
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.58
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.82
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  440.10
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.40
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.26
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.84
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.46
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4867.09
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.18
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.91
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.47
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.55
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.52
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.73
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.05
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.13
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -1.13
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:26.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.04
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    2.32
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:02:26.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 2.06e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.49e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 8.40e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.22
p-value of test                       :    0.9964

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.19
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   42.00
p-value of test                       :  1.1e-3



-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:06.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10009.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.85
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.098
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:04:22.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4987.39
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.13
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:57.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4259.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.35
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11999.83
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.66
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:32.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.29
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999972512

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.19
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000025177

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:11.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:15.73

 All tests were passed




Server wird beendet - Lösche Semaphor 108494866.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:52.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:58.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:58.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7146
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:08.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:09.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:06.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:11.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:14.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:42.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.88
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.66
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.47
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.46
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:53.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1340.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:02.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6840.84
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:55.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.80
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.78
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.08
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  149.94
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:38.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4985.48
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:56.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46076
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870076
  j =  1                              :        399907849
  j =  2                              :            46074
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45709
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869709
  j =  1                              :        399908587
  j =  2                              :            45699
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9946

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:31.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:19.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:49.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.14e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.95
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.68
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.75
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.58
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.13
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.12
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.70
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17442.85
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.34
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.41
p-value of test                       :    0.9905


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.56
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.39
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.16
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.97
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.49
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.91
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.86
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.39
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.71
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.28
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.32
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.13
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.84
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.59
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.93
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.17
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.67
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.79
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.21
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.19
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.36
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.54
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.98
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.31
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.55
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4785.40
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.79
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.40
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.45
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:24.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.90
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -1.46
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:23.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.29
p-value of test                       :    0.01

Sample variance                       :    2.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.61e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.31
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.27
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.14
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:05.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.01
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:06.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10099.46
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.8e-3

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10337.95
p-value of test                       :  8.9e-3

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.34
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:04:19.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4764.61
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:55.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3932.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.36
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11668.47
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:32.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.01
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.82
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000100333

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.20
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999982748

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.35e-3
p-value of test                       :    0.9976

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.61
p-value of test                       :    0.9955

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:30.50

 All tests were passed




Server wird beendet - Lösche Semaphor 109510674.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5464
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:53.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4463
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:57.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:06.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:09.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:05.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:07.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.03
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    2.58
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     258
p-value of test                       :    0.9928

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:15.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:43.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.55
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.86
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.78
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.96
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.03
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.80
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.71
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.18
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:54.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1539.62
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7017.21
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.98
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:14.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.78
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.09
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.26
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:58.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46043
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870043
  j =  1                              :        399907917
  j =  2                              :            46037
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45796
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869796
  j =  1                              :        399908409
  j =  2                              :            45794
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:30.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:19.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:51.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:37.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 6.54e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.23e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.075
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:47.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.47
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.23
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.62
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.69
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.92
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.11
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.49
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.53
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.28
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.08
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17440.55
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.69
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.92
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.33
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.32
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.13
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.11
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.06
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.36
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.68
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.16
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.58
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.96
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.33
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.07
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.20
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.06
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.09
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.73
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.27
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.29
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5037.73
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.48
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.01
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.30
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.10
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4884.75
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.26
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.17
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.17
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:24.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.97
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.58e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.17
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.23
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:04.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.45
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:04.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.79
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10095.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:04:12.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.37
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:52.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.32
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.16
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.23
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11989.98
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:32.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11630.48
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:32.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.60
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000033217

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.20
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000045289

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:38.79

 All tests were passed




Server wird beendet - Lösche Semaphor 110559250.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5474
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:54.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:40.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4467
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:05.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:06.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:56.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:01.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9915

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:14.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    2.14
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:44.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.60
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.51
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.40
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.30
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.49
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1381.96
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6958.27
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.89
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:04.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.98
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.08
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5114.26
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:55.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45971
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869971
  j =  1                              :        399908060
  j =  2                              :            45967
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46303
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870303
  j =  1                              :        399907395
  j =  2                              :            46301
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:28.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:18.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.069
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:39.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.69
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:48.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.02
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.17
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.06
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.38
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17431.61
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.16
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.47
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.57
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.17
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.49
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.19
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.89
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.04
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.45
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.61
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.35
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.73
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.73
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.86
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.80
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  563.26
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.36
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.88
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.64
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.66
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.12
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.15
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.86
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.85
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.12
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.68
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.42
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.25
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.92
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:24.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.97
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:22.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.06e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 7.51e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.81
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.39
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:05.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.22
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:03.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.11
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10094.56
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:37.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.63
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.53
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.31
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.00
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12148.62
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.57
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999966788

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.23
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000099214

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.16
p-value of test                       :    0.9977

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:33.81

 All tests were passed




Server wird beendet - Lösche Semaphor 111607826.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5362
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:53.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4126
p-value of test                       :    0.9994    *****


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:40.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:57.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:05.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:55.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.86
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.00
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     857
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:14.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    2.05
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     176
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:39.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.40
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.16
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.66
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  474.77
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:43.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.67
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6955.41
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:41.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.88
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.61
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:02.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.78
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:33.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4925.91
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:54.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45887
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869887
  j =  1                              :        399908229
  j =  2                              :            45881
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45789
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869789
  j =  1                              :        399908423
  j =  2                              :            45787
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:27.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:17.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:59.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.14e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 3.01e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.98e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:39.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.75
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.79
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.44
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.84
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.41
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.16
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.08
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.64
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.71
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.36
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.72
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 3.64e-3
p-value of test                       :    0.9962

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.2e-3

Anderson-Darling statistic = A2       :    4.35
p-value of test                       :  6.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17961.13
p-value of test                       :  2.4e-3



-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.57
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.28
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.19
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.09
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.34
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.71
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.96
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.37
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.49
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.69
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.94
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.31
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.95
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.04
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.87
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.34
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.77
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.45
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.90
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.97
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.95
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.03
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.16
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.92
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.18
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.73
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4896.25
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.19
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.45
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.67
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   0.097
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.54
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:23.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 5.01e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.70
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.01
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:05.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.50
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:04.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10171.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.56
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : 2.11e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:37.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:46.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4731.77
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4242.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3970.45
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11953.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11965.66
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.63
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999983171

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.49
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999994016

Normal statistic for number of bits   :  -0.047
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:17.44
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 14  BirthdaySpacings, t = 3         0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 112623634.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1270
p-value of test                       :    0.9948

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334390
  j =  1                              :        599997460
  j =  2                              :             1270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:54.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:43.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:01.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:08.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:10.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.73
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     334
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:12.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:40.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.37
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.39
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.21
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.02
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.96
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.98
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1474.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:07.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6982.25
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.71
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.6e-3

Anderson-Darling statistic = A2       :    3.98
p-value of test                       :  9.3e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:16.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.83
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.87
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:39.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5015.42
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:57.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46076
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870076
  j =  1                              :        399907850
  j =  2                              :            46072
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45784
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869784
  j =  1                              :        399908433
  j =  2                              :            45782
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:29.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:19.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:10.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:05.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:25.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:51.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.22
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.43
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.89
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.43
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.14
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.35
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17389.05
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.39
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.03
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.28
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.90
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.09
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.24
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.20
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.02
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.02
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  440.21
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.23
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.10
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.18
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.75
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.36
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.15
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.21
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.08
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.44
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.66
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.99
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.02
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.65
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.48
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.25
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.53
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.82
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.85
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.94
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :    1.79
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:23.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
p-value of test                       :    0.9913

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.59e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 6.66e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.00e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.28
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.61
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.49
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:05.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.13
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:04.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10253.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9901.11
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:04:19.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4769.52
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.60
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.49
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.04
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11917.09
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.02
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:33.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.22
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000013606

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.36
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000070888

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.31
p-value of test                       :    0.99

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:47.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 84  Fourier3, r = 0                 0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 113639442.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:56.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:05.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:05.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:57.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:02.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    4.17
p-value of test                       :  7.2e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     956
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     645
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:14.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:43.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.13
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.80
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.34
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.09
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.51
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.86
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.12
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:59.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6913.99
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:40.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.91
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:04.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.22
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   88.72
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5208.45
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:58.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45702
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869702
  j =  1                              :        399908600
  j =  2                              :            45694
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46104
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870104
  j =  1                              :        399907797
  j =  2                              :            46094
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:27.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:17.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:54.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.23e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.88e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:35.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:38.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.25
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.18
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.83
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.88
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.41
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.59
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17485.34
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.08
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.42
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.24
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.48
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.15
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.71
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.73
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.73
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.54
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.54
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.70
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.84
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   95.92
p-value of test                       :    0.9963


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.50
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.84
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  431.61
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  100.26
p-value of test                       :    0.9906


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.46
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.48
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.79
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5125.42
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.22
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.40
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.57
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.33
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4892.19
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.97
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.80
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.12
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    1.55
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:21.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.75
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -1.00
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    0.22
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 8.76e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.42
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.81
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:03.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:04.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.56
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.49
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.072
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:40.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.86
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5024.92
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:51.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.73
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.26
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11781.07
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.61
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999904001

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.87
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000050836

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.031
p-value of test                       :    0.49

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:19.05

 All tests were passed




Server wird beendet - Lösche Semaphor 114688018.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5314
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:55.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:43.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4445
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:01.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:11.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:01.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7165
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:15.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:43.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.97
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.57
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.44
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  272.04
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  386.97
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:03.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1328.76
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:02.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6942.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:13.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.97
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:08.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.88
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.24
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:36.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5093.66
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:57.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45844
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869844
  j =  1                              :        399908317
  j =  2                              :            45834
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45626
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869626
  j =  1                              :        399908750
  j =  2                              :            45622
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 2.68e-3
p-value of test                       :    0.9970

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.39
p-value of test                       :  5.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  9.7e-4    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:30.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:02.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 2.89e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.58
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.13
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.63
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.40
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.88
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.39
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17443.87
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.19
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.15
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.72
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   36.73
p-value of test                       :  3.7e-3


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.58
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.32
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.75
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.15
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.89
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.96
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.45
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.15
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.80
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.83
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.04
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.08
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.35
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.44
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.43
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.90
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.37
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.40
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.93
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.43
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.34
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.13
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5158.91
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.93
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.39
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.14
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :  -0.019
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.11
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :   -1.84
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 7.82e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 3.44e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.60
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.21
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.85
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:10.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.40
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:11.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.51
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    3.01
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:04:06.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.89
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:51.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5044.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:53.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3995.06
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.47
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.84
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:29.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12050.72
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:30.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.87
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000030436

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.66
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999792260

Normal statistic for number of bits   :   -1.64
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.13
p-value of test                       :    0.02

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :  -0.080
p-value of test                       :    0.53

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:36.52
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 46  MaxOft, t = 8                   9.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 115703826.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5520
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:56.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:57.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7146
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:07.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:07.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:00.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:04.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.55
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     949
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.05
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.92
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:16.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:43.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.65
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.88
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.64
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.19
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.67
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.24
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.54
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.66
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.33
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.10
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:04.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7057.88
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.28
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.97
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:09.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.82
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.76
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5014.62
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:58.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45881
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869881
  j =  1                              :        399908241
  j =  2                              :            45875
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45519
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869519
  j =  1                              :        399908963
  j =  2                              :            45517
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:30.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.51e-3
p-value of test                       :    0.9949

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  7.5e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:01.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.38e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 2.04e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.46
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.70
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.70
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.51
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.06
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.60
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17408.14
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.20
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.28
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.17
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.38
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.97
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.90
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.26
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.03
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.99
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.22
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.00
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.79
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.55
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.93
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.60
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.50
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.41
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.79
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.46
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.16
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5130.82
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.56
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.06
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:34.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.88
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.65
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.58
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.00
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.30
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:19.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.61
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:21.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 5.07e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.02e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 6.38e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.99
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.62
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.61
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:04.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.42
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:05.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.82
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10131.30
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:04:10.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.95
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:52.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4695.36
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:52.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.33
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4308.63
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11995.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11615.67
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.30
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000067618

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.13
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000087751

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.077
p-value of test                       :    0.47

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:26.60

 All tests were passed




Server wird beendet - Lösche Semaphor 116719634.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:49.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5422
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:55.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:05.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:55.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:00.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.00
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:14.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.07
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.91
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.53
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.02
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.01
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.24
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  191.70
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.35
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:43.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7045.88
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.57
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.83
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:03.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.41
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.87
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5229.18
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:04.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45802
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869802
  j =  1                              :        399908400
  j =  2                              :            45794
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46519
p-value of test                       :  1.5e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870519
  j =  1                              :        399906964
  j =  2                              :            46515
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:27.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:18.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:59.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.39e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:38.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.51
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:47.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.78
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.24
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:38.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.76
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.50
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.04
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17287.13
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.79
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.61
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.44
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.24
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.39
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.68
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.18
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.18
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.25
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.33
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.08
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.66
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.44
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.00
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.23
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.85
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.61
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.54
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.40
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.01
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.80
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5148.46
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.27
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.12
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.92
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.29
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.76
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.81
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.10
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.99
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.39
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.05
p-value of test                       :    0.02

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 3.77e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 6.08e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.51
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.02
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.23
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:04.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:04.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10186.21
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10203.77
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:40.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.21
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.45
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.85
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11694.25
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11566.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.42
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999901493

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.34
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999933572

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:28.25

 All tests were passed




Server wird beendet - Lösche Semaphor 117735442.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5484
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:55.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:05.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:56.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:01.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9945

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.64
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:16.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:43.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.58
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.44
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.47
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.20
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  262.60
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1539.74
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:00.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7239.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:41.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.76
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:03.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.81
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.46
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4851.28
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:00.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46277
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870277
  j =  1                              :        399907449
  j =  2                              :            46271
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45799
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869799
  j =  1                              :        399908407
  j =  2                              :            45789
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:27.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:18.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:58.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:37.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.84e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 3.41e-4
p-value of test                       :  9.5e-3

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:37.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.034
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:35.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.99
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.06
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.97
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.61
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.99
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.91
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.27
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17310.90
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.93
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.84
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.24
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.53
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.98
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.07
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.64
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.50
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.67
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.59
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.53
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.13
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  100.51
p-value of test                       :    0.9902


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.66
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.48
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :   97.78
p-value of test                       :    0.9992    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.08
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.75
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.82
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.97
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.05
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.09
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.37
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.96
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.92
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5147.31
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  314.51
p-value of test                       :    0.9924


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.37
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.80
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    1.34
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:21.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.48
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:22.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.79e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 8.51e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.69e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.45
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.57
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.00
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:05.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.55
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9972.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:37.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.78
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:46.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.28
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.85
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.91
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11391.17
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11778.42
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.37
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000126988

Normal statistic for number of bits   :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.42
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999947303

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:02.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 M (L=1000, r=20)    0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 118685714.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:48.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5406
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:54.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4231
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:04.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:03.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:54.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:59.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9941

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.35
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    2.29
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    2.64
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:16.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:45.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.94
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.63
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.95
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.32
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.61
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6995.33
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.65
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:04.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.62
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.31
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:00.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45974
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869974
  j =  1                              :        399908055
  j =  2                              :            45968
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46036
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870036
  j =  1                              :        399907929
  j =  2                              :            46034
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:28.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 8.05e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.66e-3
p-value of test                       :    0.9959

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  7.5e-3

Anderson-Darling statistic = A2       :    4.62
p-value of test                       :  4.5e-3


-----------------------------------------------
CPU time used                    :  00:02:19.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  1.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.82e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.43e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:38.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.95
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.79
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.92
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.80
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  167.89
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17597.95
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.44
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.78
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.56
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.13
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.07
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.57
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.48
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.75
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.59
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.01
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.32
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.11
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.72
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.91
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.52
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.03
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  100.56
p-value of test                       :    0.9901


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.21
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.79
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.42
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.76
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.72
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.61
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5076.45
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.49
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.29
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.02
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -1.48
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:21.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.60
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 7.01e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.08
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.31
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.92
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:05.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.77
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:05.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10113.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:40.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.60
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.67
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4257.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.70
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.12
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11672.72
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:29.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.23
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000005458

Normal statistic for number of bits   :   0.043
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.79
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000033958

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:44.44

 All tests were passed




Server wird beendet - Lösche Semaphor 119701522.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:48.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.58

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:55.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:04.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:05.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:56.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:02.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    4.41
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:02:16.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:46.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.14
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.45
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.54
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.52
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.05
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.45
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.27
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1492.23
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7274.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.10
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:03.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.44
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.37
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4872.80
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:00.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45783
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869783
  j =  1                              :        399908438
  j =  2                              :            45775
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45587
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869587
  j =  1                              :        399908827
  j =  2                              :            45585
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:28.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:19.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:59.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 2.98e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:36.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:36.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.09
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.48
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.06
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:48.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.07
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.53
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.96
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.98
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17497.26
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.97
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.17
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.97
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.88
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.81
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.64
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.50
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.72
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.69
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.75
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.90
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.78
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.21
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.58
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.44
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.66
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.77
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.98
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.02
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.23
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.25
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.41
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  447.66
p-value of test                       :  7.8e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.22
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.88
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.38
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4884.70
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.28
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.96
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.34
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.71
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:21.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
p-value of test                       :    0.9939

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.21
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.30
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:05.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.99
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9818.20
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.73
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.024
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:39.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.03
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.17
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:51.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4006.05
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4204.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.45
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11657.64
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.02
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000125359

Normal statistic for number of bits   :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.78
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000058756

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:22.92

 All tests were passed




Server wird beendet - Lösche Semaphor 120717330.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5297
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:55.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:04.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:05.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:55.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:01.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.88
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    3.61
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    3.84
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    2.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:14.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    2.10
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:44.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.36
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.97
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.26
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.88
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.54
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.00
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.42
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.42
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6925.08
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.97
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.21
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:04.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.49
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.24
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5010.13
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:56.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45507
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869507
  j =  1                              :        399908989
  j =  2                              :            45501
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45875
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869875
  j =  1                              :        399908255
  j =  2                              :            45865
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:28.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 8.97e-4
p-value of test                       :    0.9991    *****

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  4.2e-3

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  3.2e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:20.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:53.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 6.65e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:33.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.09
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:47.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.88
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.21
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   52.96
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.56
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:10.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.39
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17251.80
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.28
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.46
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.23
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.71
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.51
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.11
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.86
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.39
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.13
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.48
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.08
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.87
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.56
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.63
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.52
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.44
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.92
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.69
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.90
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.52
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.38
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.29
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.29
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.69
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.99
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:33.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.74
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.86
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.28
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  429.81
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.05
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.78
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:12.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.19
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:12.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.97e-3
p-value of test                       :    0.9948

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.95
p-value of test                       :    0.97

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.59e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.21e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 5.76e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.87
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.66
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.04
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.76
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:56.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.07
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9829.52
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : 3.51e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:22.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4773.56
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.14
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.99
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4235.99
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.84
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.02
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000187570

Normal statistic for number of bits   :    1.48
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.52
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999879770

Normal statistic for number of bits   :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 3.73e-3
p-value of test                       :    0.9961

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.04
p-value of test                       :    0.02

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:56:53.04

 All tests were passed




Server wird beendet - Lösche Semaphor 121667602.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5487
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:43.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:36.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:36.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:06.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:07.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:04.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:10.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.07
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:10.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:45.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.74
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.11
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.08
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.53
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.72
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.10
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.08
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.45
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:08.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7163.80
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:57.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-3
p-value of test                       :    0.9977

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   91.86
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:03:12.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.24
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.20
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:41.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5238.99
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9957


-----------------------------------------------
CPU time used                    :  00:03:11.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45630
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869630
  j =  1                              :        399908744
  j =  2                              :            45622
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46103
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870103
  j =  1                              :        399907798
  j =  2                              :            46095
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9949


-----------------------------------------------
CPU time used                    :  00:02:32.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:18.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:06.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:57.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:39.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 2.50e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.45e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:51.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.41
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.51
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.61
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:51.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.01
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.45
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:53.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.26
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.62
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.41
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.75
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17630.92
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.84
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.31
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.10
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.98
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.64
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.00
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.89
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.98
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.38
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.08
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.04
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.37
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  103.85
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.74
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.34
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.80
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.82
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.25
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.88
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.67
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.07
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.71
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.91
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.90
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.22
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.39
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.32
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.23
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:24.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.33
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -1.84
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:25.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.26e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.46e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.35
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.95
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.74
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:05.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9936

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  2.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9661.96
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9767.01
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.34
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:04:34.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.87
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:52.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4983.76
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4240.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.44
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12081.07
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:35.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11665.01
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:36.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.81
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000112570

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.21
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000038344

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.091
p-value of test                       :    0.46

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:19:14.36

 All tests were passed




Server wird beendet - Lösche Semaphor 102203411.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:49.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:38.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:03.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:04.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:09.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:15.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    2.44
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:45.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.54
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.97
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.47
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.97
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.64
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.66
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.66
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:29.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:52.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1368.65
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:04.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7215.53
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.01
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:13.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.17
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   88.39
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:37.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.97
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:54.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46192
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870192
  j =  1                              :        399907622
  j =  2                              :            46180
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45715
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869715
  j =  1                              :        399908575
  j =  2                              :            45705
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:30.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:17.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.11e-3
p-value of test                       :    0.9989

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:01.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.28e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 1.65e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.87e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 7.27e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.45
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.56
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.65
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.05
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.11
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.22
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17705.99
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.60
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.86
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.44
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.23
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.18
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.03
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.10
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.59
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.20
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.24
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.10
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.05
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.79
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.74
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.46
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.72
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.16
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.96
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.53
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.19
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4832.24
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.74
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.11
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.72
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.22
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5118.54
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.04
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.25
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.66
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:24.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.55
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    1.78
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:24.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         : -5.43e-3
p-value of test                       :    0.50

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.28e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.95e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.39
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.41
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.83
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:06.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.36
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.78
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.13
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:04:18.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.58
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:53.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.74
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4025.93
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.94
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.78
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:29.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.47
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000060643

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.85
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999911057

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.077
p-value of test                       :    0.47

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:05.48

 All tests were passed




Server wird beendet - Lösche Semaphor 103514131.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5426
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:49.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:39.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:37.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:55.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4213
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:05.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7506
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:55.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:00.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    3.62
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    2.44
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     651
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     334
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:11.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:38.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.80
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.18
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.33
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.88
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.25
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.53
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.18
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.21
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6975.98
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:43.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.02
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.93
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:03.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.28
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.57
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:33.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5193.11
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:55.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45722
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869722
  j =  1                              :        399908558
  j =  2                              :            45718
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46140
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870140
  j =  1                              :        399907723
  j =  2                              :            46134
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:26.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:18.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:46.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  1.9e-3

Anderson-Darling statistic = A2       :    4.07
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:53.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:32.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.31e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.78e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 9.90e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:39.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.59
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.71
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.98
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.28
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.10
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.72
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:29.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.16
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17532.58
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.10
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.38
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.00
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.37
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.28
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.71
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.33
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.02
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.57
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.00
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.02
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.24
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.80
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.22
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.27
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.19
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.46
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.40
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.86
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.88
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.32
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.87
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.14
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.85
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.84
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.78
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4821.24
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.55
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.39
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.47
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:22.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.03
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:22.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.99e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.82
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.57
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:05.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.83
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9708.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:41.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5078.74
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3926.88
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.81
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11584.13
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.77
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999975992

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.85
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999922940

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:01.54

 All tests were passed




Server wird beendet - Lösche Semaphor 104529939.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5513
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:49.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:37.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:55.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:05.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:04.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:56.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7098
p-value of test                       :    0.9951


-----------------------------------------------
CPU time used                    :  00:04:01.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    2.06
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    2.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    4.56
p-value of test                       :  4.7e-3

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:12.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:41.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.81
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.64
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.74
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.09
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.99
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.64
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.59
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.67
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.78
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:44.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.23
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7013.39
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.10
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.97
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:04.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.77
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.13
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5185.29
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:09.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45968
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869968
  j =  1                              :        399908070
  j =  2                              :            45956
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45550
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869550
  j =  1                              :        399908903
  j =  2                              :            45544
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:26.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:16.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:53.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.96e-3
p-value of test                       :    0.9933

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:31.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.48e-4
p-value of test                       :  7.9e-3

Kolmogorov-Smirnov- statistic = D-    : 3.76e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    4.56
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.24e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.54e-5
p-value of test                       :    0.9906

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:37.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:40.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.03
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.17
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.46
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.85
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.77
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.64
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17700.60
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.09
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.70
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.70
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.57
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.17
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.48
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.54
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.48
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.86
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.35
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.67
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.07
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.07
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.78
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.28
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.95
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.66
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.63
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.39
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.72
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.58
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.39
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.46
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.90
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.25
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.82
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4793.85
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.09
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.96
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.21
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:24.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.48
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:24.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.43e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 6.75e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.09
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.67
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:07.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.33
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:08.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9922.46
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.55
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.072
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:46.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.79
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.61
p-value of test                       :  2.3e-4    *****

Anderson-Darling statistic = A2       :    5.64
p-value of test                       :  1.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5164.16
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:50.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.33
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4160.37
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11800.59
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11641.13
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.61
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000112072

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   86.02
p-value of test                       :  3.6e-3


-----------------------------------------------
Total number of bits:  8000045127

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         : -9.20e-4
p-value of test                       :    0.50

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:54.61

 All tests were passed




Server wird beendet - Lösche Semaphor 105480211.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5387
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:49.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:36.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4473
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:04.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:04.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:55.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:01.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.37
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:12.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:43.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.37
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.17
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.22
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.73
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.81
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  267.75
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  476.02
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1541.69
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:00.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7067.43
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.91
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.30
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:03.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.66
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   79.79
p-value of test                       :    0.9978


-----------------------------------------------
CPU time used                    :  00:01:33.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5149.17
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:58.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908165
  j =  2                              :            45913
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45865
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869865
  j =  1                              :        399908270
  j =  2                              :            45865
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:27.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:19.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9942

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 3.88e-3
p-value of test                       :    0.9958

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:53.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.53e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 7.86e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.38
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:35.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.86
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.64
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.87
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.53
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.18
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.66
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.28
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.75
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.97
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17535.37
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.96
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.63
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.79
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.27
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.07
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.90
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.11
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.60
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.09
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.54
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.02
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  559.82
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.56
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.56
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.59
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.81
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  173.50
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.91
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.82
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.50
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.38
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.54
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.21
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.86
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.70
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.90
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.94
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.98
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.58
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.02
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -1.23
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:24.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :  -0.098
p-value of test                       :    0.54

Sample variance                       :    0.46
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 9.64e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.56e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 8.56e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.39
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.55
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.29
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:08.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.16
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.49
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:44.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.63
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4979.37
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.74
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4051.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11430.32
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.42
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.18
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999864488

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.23
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999927884

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:04.19

 All tests were passed




Server wird beendet - Lösche Semaphor 106397715.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1513
p-value of test                       :  3.9e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334633
  j =  1                              :        599996974
  j =  2                              :             1513
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5328
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:49.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:38.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:36.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:04.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:55.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:04:02.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.86
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    3.80
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:13.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:43.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.49
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.27
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.10
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.54
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.87
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.52
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.79
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.98
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:42.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7140.24
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.51
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:03.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.03
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.27
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5086.73
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:53.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46234
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870234
  j =  1                              :        399907534
  j =  2                              :            46230
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46528
p-value of test                       :  1.3e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870528
  j =  1                              :        399906949
  j =  2                              :            46518
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:26.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:17.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:01.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:54.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.99e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:34.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.80
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.14
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.55
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.65
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.69
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:41.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.38
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.01
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.99
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17168.32
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.08
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.94
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.05
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.51
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.25
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.91
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.50
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.42
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.08
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.83
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.51
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.28
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.60
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.22
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.02
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.36
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.41
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.54
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.22
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.26
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.30
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5103.54
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.47
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.95
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.06
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.02
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4877.58
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.03
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.98
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.02
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -0.60
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:24.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.07
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    1.46
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 7.86e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.20
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.86
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:07.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.20
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:09.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10052.94
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10196.45
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:39.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.38
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.23
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:50.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3999.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4235.72
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12113.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.42
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.20
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000125944

Normal statistic for number of bits   :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.88
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000102676

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:58.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           3.9e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 107380755.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1260
p-value of test                       :    0.9977

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334380
  j =  1                              :        599997480
  j =  2                              :             1260
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5411
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:50.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:38.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:36.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:55.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:03.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:04.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:55.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:00.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.87
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    4.41
p-value of test                       :  5.5e-3

Stat. AD after spacings (mNP2-S)      :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.81
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:12.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.06
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.86
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.69
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.41
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.24
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.31
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  380.58
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:42.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7002.98
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.48
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:03.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.66
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.43
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:33.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4910.59
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:56.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45587
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869587
  j =  1                              :        399908829
  j =  2                              :            45581
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45599
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869599
  j =  1                              :        399908803
  j =  2                              :            45597
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:27.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:01.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:53.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.67e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.064
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.93
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.96
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.41
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.88
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:37.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.56
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.36
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17156.03
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.70
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.84
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.73
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.16
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.22
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.02
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.59
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.51
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.62
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.35
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.98
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.27
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.56
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.93
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.90
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.78
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.02
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.08
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.64
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.71
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.99
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.72
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4896.02
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.94
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.43
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.39
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.14
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5023.36
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.75
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.68
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.66
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -1.63
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:24.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.03
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 2.29e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.24
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.59
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.89
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:07.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.35
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:42.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.46
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.76
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4260.25
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12107.35
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12049.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.66
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000024934

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.66
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999957878

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.078
p-value of test                       :    0.47

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:07.01

 All tests were passed




Server wird beendet - Lösche Semaphor 108396563.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5358
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:52.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:37.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:06.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:05.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:57.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:00.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    2.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:13.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:42.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.63
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.30
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.31
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.01
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.67
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.07
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.00
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:05.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6917.18
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.27e-3
p-value of test                       :    0.9956

Kolmogorov-Smirnov- statistic = D-    :    0.69
p-value of test                       :  1.2e-5    *****

Anderson-Darling statistic = A2       :    7.79
p-value of test                       :  1.6e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :  106.10
p-value of test                       :  2.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:03:09.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.04
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.31
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5069.14
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:55.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45616
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869616
  j =  1                              :        399908772
  j =  2                              :            45608
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45652
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869652
  j =  1                              :        399908697
  j =  2                              :            45650
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:28.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:16.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:00.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.35
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:37.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.92e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.96e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:41.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.63
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.23
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.98
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.92
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:45.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.45
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.31
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.53
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17123.52
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.64
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.18
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.68
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.10
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.76
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.06
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.85
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.41
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.52
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.13
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.82
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.45
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.41
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.28
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.39
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.40
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.90
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.76
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.47
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.50
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.17
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.92
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.05
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.28
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.26
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4772.42
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  317.33
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.56
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.25
p-value of test                       :    0.9935


-----------------------------------------------
Normal statistic for number of jumps  :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:23.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.83
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:23.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    2.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.74e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.91e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.67
p-value of test                       :  8.1e-3

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.02
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.68
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:07.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.31
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10070.14
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.068
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:04:15.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.72
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:52.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4729.01
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:53.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.07
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.78
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11642.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.39
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000000286

Normal statistic for number of bits   : 2.26e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.51
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999996107

Normal statistic for number of bits   :  -0.031
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:04.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 39  Run, r = 15                     2.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 109281299.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:51.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:39.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4435
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:55.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:01.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    3.27
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     962
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    3.38
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:13.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:44.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.17
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.98
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   86.23
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.08
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.26
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:43.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.92
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6983.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.41
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:03.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.29
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.00
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:34.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5239.06
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:58.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45731
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869731
  j =  1                              :        399908540
  j =  2                              :            45727
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46009
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870009
  j =  1                              :        399907984
  j =  2                              :            46005
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:27.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:17.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:01.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:34.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.16e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 3.37e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 8.82e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.09
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.33
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.96
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.89
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:38.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.98
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.29
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17361.32
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.76
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.72
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.88
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.58
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.67
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.72
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.05
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.31
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.70
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.55
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.41
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.30
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.17
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.71
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.40
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.46
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.77
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.48
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.49
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.06
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.16
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.29
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5069.14
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.76
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.42
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.74
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.74
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4931.73
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.37
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.36
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:22.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.32
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:22.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.85e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 8.40e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 7.05e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.73
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.29
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:07.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.52e-3
p-value of test                       :    0.9942

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.74
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:09.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10183.02
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10048.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:39.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.65
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:48.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.53
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:50.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.29
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.83
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12027.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.81
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000117181

Normal statistic for number of bits   :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.98
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999974189

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:12.45

 All tests were passed




Server wird beendet - Lösche Semaphor 110395411.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1251
p-value of test                       :    0.9990    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334371
  j =  1                              :        599997498
  j =  2                              :             1251
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5483
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:52.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:39.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:39.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:04.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:59.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:13.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:41.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.73
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.04
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.77
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.07
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   85.96
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.26
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:43.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1378.95
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6902.09
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.23
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:03.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.65
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.16
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:34.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4993.01
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:57.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45789
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869789
  j =  1                              :        399908425
  j =  2                              :            45783
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45773
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869773
  j =  1                              :        399908456
  j =  2                              :            45769
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:27.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.31e-4
p-value of test                       :    0.9997    *****

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  4.0e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:18.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.61e-3
p-value of test                       :    0.9912

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:01.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:54.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 9.26e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.79e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:38.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:35.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.74
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.24
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.05
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.03
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.55
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.92
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.10
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.74
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17533.08
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   16.93
p-value of test                       :    0.9971


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.97
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.22
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.38
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.71
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.60
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.59
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.23
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.70
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.61
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.32
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.72
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.27
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.80
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.39
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.32
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.49
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.47
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.12
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.04
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.14
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  442.64
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.37
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.38
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.81
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4822.75
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.72
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.83
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.62
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.12
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:22.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.75
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.41
p-value of test                       :    0.9920

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.39
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.07
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.99
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:07.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.72
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.75
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:42.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5022.23
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.05
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:50.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.32
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.64
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11973.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.06
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000010345

Normal statistic for number of bits   :   0.082
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.96
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000157675

Normal statistic for number of bits   :    1.25
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   0.040
p-value of test                       :    0.48

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:02.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14           0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 111345683.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5369
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:51.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:39.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:38.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:05.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:55.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:01.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     856
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.29
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:13.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.47
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.60
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.21
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.28
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.53
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.73
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.12
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1501.44
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7235.09
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.87
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:03.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.46
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.96
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:33.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.20
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:54.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45937
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869937
  j =  1                              :        399908129
  j =  2                              :            45931
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45924
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869924
  j =  1                              :        399908156
  j =  2                              :            45916
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:18.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:02.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:33.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.49e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 4.19e-4
p-value of test                       :  8.8e-4    *****

Anderson-Darling statistic = A2       :    4.15
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:38.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   98.67
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   96.82
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.22
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.84
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.29
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.52
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.90
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.37
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.16
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.38
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17482.58
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.86
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.37
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.88
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.08
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.65
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.17
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.80
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.94
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.56
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.96
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.71
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.73
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.03
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.44
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.47
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.35
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.83
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.99
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.11
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.48
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.21
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.89
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.36
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.88
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.86
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.43
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.16
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5118.63
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.82
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.93
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.07
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:25.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.70
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:23.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9953

Tests on the sum of all N observations
Standardized normal statistic         :  -0.049
p-value of test                       :    0.52

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 7.07e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.67
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.40
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.60
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:05.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.96
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:06.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10096.15
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9779.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:41.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:47.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5045.26
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:50.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4268.76
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12045.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11561.82
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.57
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000006544

Normal statistic for number of bits   :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.74
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999979469

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:45.85

 All tests were passed




Server wird beendet - Lösche Semaphor 112263187.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1480
p-value of test                       :  1.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334600
  j =  1                              :        599997040
  j =  2                              :             1480
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:54.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:39.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7120
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:04.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:04.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7483
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:55.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:00.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:12.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    2.10
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:40.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.93
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.16
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.52
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.81
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:01.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7161.23
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.25
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.44
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:04.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.07
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.02
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4998.15
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:59.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45632
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869632
  j =  1                              :        399908741
  j =  2                              :            45622
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45765
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869765
  j =  1                              :        399908476
  j =  2                              :            45753
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:27.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:18.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:01.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:55.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:33.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.90e-4
p-value of test                       :  2.3e-3

Kolmogorov-Smirnov- statistic = D-    : 8.13e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.064
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.30
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.17
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.91
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.67
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.49
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.96
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.90
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.15
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17304.46
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.98
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.55
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.22
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.64
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.47
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.84
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.56
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.03
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.79
p-value of test                       :    0.9904


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.20
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.98
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.78
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.22
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.47
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.75
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.67
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.46
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.83
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.00
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.64
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.05
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.03
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.51
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.71
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.27
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5148.42
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  442.54
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.38
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.78
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:22.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.27
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:22.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.02e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.35e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.87
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.39
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:05.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.55
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:06.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10023.39
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10131.35
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:42.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4789.61
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.20
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:50.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.57
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4223.06
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11713.92
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11976.63
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   91.71
p-value of test                       :  1.0e-3


-----------------------------------------------
Total number of bits:  7999850316

Normal statistic for number of bits   :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.39
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999906464

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :  -0.026
p-value of test                       :    0.51

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:16.92

 All tests were passed




Server wird beendet - Lösche Semaphor 113213459.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5504
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:53.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:03.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:54.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:59.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    3.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:15.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    6.08
p-value of test                       :  9.1e-4    *****

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:45.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.94
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.18
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.99
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.33
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.67
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:44.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7135.64
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:41.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.02
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.90
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:03.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.62
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.26
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:33.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5064.88
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:57.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46009
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870009
  j =  1                              :        399907984
  j =  2                              :            46005
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45964
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869964
  j =  1                              :        399908075
  j =  2                              :            45958
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:28.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:17.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:34.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 9.11e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.060
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:39.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.55
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:47.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.76
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.91
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.12
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.30
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.40
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.42
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:38.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.22
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.00
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.75
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.95
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17643.16
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.67
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.96
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.73
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.99
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.44
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.28
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.78
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.07
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.93
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.29
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.33
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.10
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.54
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.96
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.71
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.59
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.63
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.36
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.62
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.55
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.03
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.95
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5053.81
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.40
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.52
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.81
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.89
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:21.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    2.41
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.98e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 7.01e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.42
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   40.00
p-value of test                       :  4.5e-3



-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.83
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.59e-3
p-value of test                       :    0.9919

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:07.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.19
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9840.04
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.056
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:39.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.81e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5040.00
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.87
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:50.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.67
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3998.67
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12159.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11832.58
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.19
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000111658

Normal statistic for number of bits   :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.21
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999880346

Normal statistic for number of bits   :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.22
p-value of test                       :    0.01

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:31.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP2, t = 16         9.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 114098195.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:56.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:41.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:57.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:04.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:04.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:59.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    2.94
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:15.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:44.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.32
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.53
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.12
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.97
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.44
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.56
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.50
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.31
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.62
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1374.92
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7094.05
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.48
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.40
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:03.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.13
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.49
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5051.21
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45467
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869467
  j =  1                              :        399909068
  j =  2                              :            45463
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45592
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869592
  j =  1                              :        399908822
  j =  2                              :            45580
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:27.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:18.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 7.06e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.47e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:37.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.48
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.55
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.68
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.80
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.10
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.87
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.56
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   16.25
p-value of test                       :  1.0e-3

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.85
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17456.05
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.45
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.96
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.30
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.20
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.05
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.38
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.21
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.87
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.32
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.63
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.82
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.95
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.63
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.66
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.19
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.90
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.11
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.56
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.06
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.09
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.71
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5133.08
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.79
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.64
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.81
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.19
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.31
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.88
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.55
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.84
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :  -0.051
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.41
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:21.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 8.28e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.91e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.82
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.38
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.73
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:04.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.57
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:07.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9838.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10145.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:39.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4981.23
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.46
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4219.23
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.26
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11616.87
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.73
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000141097

Normal statistic for number of bits   :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.08
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999934940

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:53.14

 All tests were passed




Server wird beendet - Lösche Semaphor 115114003.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:40.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5496
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:55.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:57.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:55.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:59.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    2.00
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    2.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:16.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:46.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.26
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.94
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.68
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.68
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.32
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.07
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7189.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:05.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.15
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.28
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5034.17
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:04.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45657
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869657
  j =  1                              :        399908690
  j =  2                              :            45649
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45943
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869943
  j =  1                              :        399908119
  j =  2                              :            45933
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:27.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:17.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :  3.1e-3

Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
p-value of test                       :    0.9901

Anderson-Darling statistic = A2       :    5.88
p-value of test                       :  1.2e-3


-----------------------------------------------
CPU time used                    :  00:02:01.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:55.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.065
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.46
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:47.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.65
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.74
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.06
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.06
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.05
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.65
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 2.66e-3
p-value of test                       :    0.9973

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17798.84
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.73
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.53
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.67
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.44
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.61
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.68
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.04
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.95
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.34
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.49
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.94
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  441.85
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.61
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.29
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.62
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  578.61
p-value of test                       :  8.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.13
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.10
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.72
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.80
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.47
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.42
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.32
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.95
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.62
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.89
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.68
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.10
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:23.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.84
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:22.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.94
p-value of test                       :    0.03

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.39
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.57
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:03.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.96
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10116.76
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10139.28
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:43.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.11
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.66
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:51.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3966.01
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.04
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11690.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:29.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.36
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999941855

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.78
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999904226

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    2.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.90e-3
p-value of test                       :    0.9927

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.80
p-value of test                       :    0.96

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:35.95

 All tests were passed




Server wird beendet - Lösche Semaphor 116064275.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9964


-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7151
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:41.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:57.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:59.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:08.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:07.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:59.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:00.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.85
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.92
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    8.12
p-value of test                       :  1.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:12.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.82
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.71
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:41.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.02
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.90
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.36
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.09
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.52
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1578.93
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:02:04.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7069.87
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.30
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:05.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.91
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.89
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5028.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:02.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45944
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869944
  j =  1                              :        399908116
  j =  2                              :            45936
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45637
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869637
  j =  1                              :        399908728
  j =  2                              :            45633
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:29.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:17.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:43.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:36.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.080
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.41
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.19
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.19
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.58
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.41
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:44.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.56
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.34
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.44
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17304.04
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.08
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.28
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.72
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.55
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.40
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.27
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.81
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.37
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.03
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.70
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.92
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.39
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.79
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.44
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.69
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.80
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.12
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.19
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.64
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.11
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.29
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.91
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.49
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.86
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.90
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.11
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.90
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.54
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.37
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:24.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.35
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:22.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.53e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.50e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 7.87e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.21
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.55
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.54
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:03.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.64
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:07.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10251.34
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9952.81
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:04:04.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.61
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:50.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.70
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:52.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.52
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.00
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11957.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11758.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.47
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999914894

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.00
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999882788

Normal statistic for number of bits   :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    2.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.89
p-value of test                       :    0.97

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:28.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP2S, t = 5         1.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 117080083.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5524
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:55.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:41.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:06.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:54.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:00.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.77
p-value of test                       :  3.8e-3

Test on the Nm values of W_{n,i}(mNP1):    2.69
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    3.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:12.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:45.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.09
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.10
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.61
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.98
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  274.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  481.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.69
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:02.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6920.46
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:41.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.51
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:03.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.54
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  157.57
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:33.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.51
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:58.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46256
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870256
  j =  1                              :        399907490
  j =  2                              :            46252
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45937
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869937
  j =  1                              :        399908130
  j =  2                              :            45929
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:27.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:20.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:59.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.23e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.20
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.60
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.62
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.80
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.68
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.89
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17537.77
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.58
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   47.85
p-value of test                       :  3.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.93
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.96
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.59
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.32
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.73
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.49
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.00
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.99
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.30
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.55
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.76
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.16
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.68
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.00
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.88
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.93
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.74
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.42
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.16
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  144.15
p-value of test                       :    0.9989


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.67
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.43
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.26
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.54
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.74
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.00
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    1.27
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:21.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.65
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:22.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 6.16e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.15e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.65
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.79
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.17
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.85
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:06.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9854.61
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.30
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:45.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:47.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.99
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:51.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.03
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.38
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11928.37
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.43
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:29.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.00
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999919676

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.33
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000024328

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   0.085
p-value of test                       :    0.47

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:52.45

 All tests were passed




Server wird beendet - Lösche Semaphor 118128659.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5386
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:57.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:57.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:05.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:05.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:55.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:00.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:18.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.93
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:47.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.45
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.42
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.54
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.11
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.97
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.04
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:44.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.29
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7039.56
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:42.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.67
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.99
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.68
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.31
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:32.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5078.37
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:00.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46317
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870317
  j =  1                              :        399907371
  j =  2                              :            46307
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45941
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869941
  j =  1                              :        399908122
  j =  2                              :            45933
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:28.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:19.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 9.43e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.92e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.08e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.17e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.85
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.68
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.58
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.62
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.88
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:40.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.95
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.75
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.13
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.44
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17731.06
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.95
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.39
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.61
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.40
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.47
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.20
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.85
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.90
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.75
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.48
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.07
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.91
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  578.82
p-value of test                       :  8.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  186.30
p-value of test                       :  2.7e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.84
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.65
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.61
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.16
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.50
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.43
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.47
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.39
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.64
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.39
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.31
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.15
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.85
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.33
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.93
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:22.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.12
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:23.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.28e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.48e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.29
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.77
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:06.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10098.49
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.60
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:39.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4790.18
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.09
p-value of test                       :  8.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4649.32
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:01:50.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4016.17
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4223.38
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11642.79
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11866.36
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.68
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999916718

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.44
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000135604

Normal statistic for number of bits   :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:34.63

 All tests were passed




Server wird beendet - Lösche Semaphor 119177235.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:56.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:05.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:55.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:00.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.65
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:15.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    2.05
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     175
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:46.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.50
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.90
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.55
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.71
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.27
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.76
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.24
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.72
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:44.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.83
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:03.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6919.12
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:44.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.02
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.60
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:05.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.97
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.10
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:33.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5048.79
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:01.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45880
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869880
  j =  1                              :        399908244
  j =  2                              :            45872
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45937
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869937
  j =  1                              :        399908129
  j =  2                              :            45931
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:28.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:18.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 8.20e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:34.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:35.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.55
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:38.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.99
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.086
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17394.03
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.84
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   57.25
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.61
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.59
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.07
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.32
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.90
p-value of test                       :    0.9927


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.43
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.05
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.23
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.13
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.38
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.44
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.55
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.77
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.88
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.83
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.00
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.68
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.54
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4799.01
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.35
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.19
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.22
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.12
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4867.32
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.88
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.66
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.01
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:22.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.56
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    1.26
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:25.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 4.77e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.62e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.13
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.08
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.86
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:05.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.28
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:04.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.31
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10060.46
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.19
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:38.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.52
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5016.52
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:50.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.41
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.93
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.00
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999947438

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.07
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000007225

Normal statistic for number of bits   :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.09

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.48e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    2.03
p-value of test                       :    0.02

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.98

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:41.56

 All tests were passed




Server wird beendet - Lösche Semaphor 120160275.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1259
p-value of test                       :    0.9979

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334379
  j =  1                              :        599997482
  j =  2                              :             1259
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:56.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:42.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:58.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:06.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:06.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7123
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:56.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:01.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     944
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    2.08
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:17.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:46.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.27
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.64
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.21
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.23
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.23
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:02.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7193.48
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:44.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :  7.1e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    5.63
p-value of test                       :  1.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   34.51
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:03:04.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.38
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.02
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:32.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5181.77
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:00.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46005
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870005
  j =  1                              :        399907995
  j =  2                              :            45995
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45988
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869988
  j =  1                              :        399908026
  j =  2                              :            45984
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:28.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:19.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:00.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.81e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.72
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.02
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   66.47
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:00:47.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.63
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.07
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.69
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.56
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17419.85
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.12
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.53
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.01
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.84
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.74
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.57
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.12
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.06
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.15
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.74
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.82
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.18
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.78
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.88
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.67
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.06
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.61
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.86
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.60
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.75
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.84
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.62
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.63
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.36
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.77
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.17
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4878.71
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.51
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.17
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.22
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:24.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.13
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :   -2.29
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:24.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.64e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 8.91e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.94e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.50
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.13
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.50
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9981

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:04.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10059.39
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9894.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:31.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.41
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:46.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.62
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4262.86
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.22
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11851.26
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.68
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000078619

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.84
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000091516

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:51.73

 All tests were passed




Server wird beendet - Lösche Semaphor 121143315.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1464
p-value of test                       :  3.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334584
  j =  1                              :        599997072
  j =  2                              :             1464
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:41.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:35.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:33.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:54.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:00.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:01.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7141
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:53.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:59.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    2.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:12.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:31.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.42
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.48
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.76
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.60
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.02
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:59.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6784.31
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.21
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.69
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:03.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.04
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.44
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:35.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4895.68
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:58.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45725
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869725
  j =  1                              :        399908553
  j =  2                              :            45719
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45996
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869996
  j =  1                              :        399908012
  j =  2                              :            45988
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:30.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:45.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.21e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.072
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:33.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.96
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.59
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.54
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.89
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:39.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.96
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.63
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17246.76
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.82
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.45
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.39
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.70
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.47
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.21
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.27
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.47
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.49
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.31
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.97
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.98
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.21
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.14
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.09
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:47.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.65
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.43
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.08
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.52
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.45
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:47.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.53
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.52
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.64
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.56
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.95
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.92
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.00
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.13
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.06
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.83
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.43
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:24.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.16
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:18.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.87

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 3.23e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.60e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 7.89e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.95
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.72
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:08.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.30
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:11.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9763.72
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.53
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:46.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5044.73
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.49
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:52.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.69
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11642.34
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12050.52
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   24.92
p-value of test                       :    0.9998    *****


-----------------------------------------------
Total number of bits:  7999919316

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.11
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999993641

Normal statistic for number of bits   :  -0.050
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.73

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.57

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:11.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 101  Run of bits, r = 0              0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 102236180.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9983


-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5323
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:43.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:37.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:34.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:54.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:54.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:00.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:01.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:52.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:58.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:44.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     260
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:11.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    2.55
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     126
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.74
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.14
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.04
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.78
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.77
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1496.86
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:59.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7154.05
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.14
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.72
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.90
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4982.67
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:58.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45851
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869851
  j =  1                              :        399908303
  j =  2                              :            45841
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45791
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869791
  j =  1                              :        399908422
  j =  2                              :            45783
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:30.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:18.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:02.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:54.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:32.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.95e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 4.35e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:34.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:34.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.33
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:47.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.86
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.81
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:47.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.27
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.89
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.51
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.53
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.93
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.92
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17510.89
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.20
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.88
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.28
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.13
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.83
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.15
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.63
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.02
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.84
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.01
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.75
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.15
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.91
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.89
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  570.43
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.69
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.27
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.50
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.10
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5127.09
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.57
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.88
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.52
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.25
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4874.85
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.05
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.68
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.02
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:23.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.79
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:20.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.00
p-value of test                       :  9.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.44
p-value of test                       :    0.9927

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.71e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.82e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 5.61e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.09
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.98
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.72
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:09.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.16
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:08.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10131.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.96
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.46
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:04:01.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4996.57
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.02
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.39
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.99
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.82
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:30.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.23
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000104551

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.35
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999934940

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:55.55

 All tests were passed




Server wird beendet - Lösche Semaphor 102793236.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:46.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4489
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:35.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:01.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:00.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:53.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:57.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    6.29
p-value of test                       :  7.3e-4    *****

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.88
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     337
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    2.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:09.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:36.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.02
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.71
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.64
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.23
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.54
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.76
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:58.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7027.01
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:04.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.02
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.88
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:34.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5040.83
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:01.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45676
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869676
  j =  1                              :        399908653
  j =  2                              :            45666
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45682
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869682
  j =  1                              :        399908638
  j =  2                              :            45678
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:29.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:18.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:02.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:54.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.85
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:32.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.03e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:33.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.93
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.94
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.63
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:47.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.97
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.58
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.30
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17241.40
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.26
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.27
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.50
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.60
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.14
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.48
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.97
p-value of test                       :    0.9924


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.03
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.70
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.42
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.08
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.68
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.44
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.12
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.13
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.72
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.63
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  577.57
p-value of test                       :  9.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.46
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.33
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.81
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.46
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.45
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.85
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.19
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.64
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.59
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5209.50
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.76
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.26
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.07
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.96
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -1.69
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:18.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.14e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 2.36e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.76
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.76
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  160.80
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.77
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:07.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10246.04
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.97
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.26
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:52.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5009.47
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.67
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11940.49
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11927.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.77
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999902951

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.59
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000010627

Normal statistic for number of bits   :   0.084
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:04.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP2, t = 5          7.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 103710740.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:50.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1472
p-value of test                       :  2.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334592
  j =  1                              :        599997056
  j =  2                              :             1472
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5304
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:51.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:36.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:01.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:01.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:53.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:10.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.83
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.20
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.77
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.50
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.30
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.54
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.97
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.36
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:59.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7230.02
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:42.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.30
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:47.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  171.04
p-value of test                       :  1.3e-3


-----------------------------------------------
CPU time used                    :  00:01:34.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5018.55
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:00.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45920
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869920
  j =  1                              :        399908162
  j =  2                              :            45916
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45972
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869972
  j =  1                              :        399908059
  j =  2                              :            45966
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:28.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:18.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:54.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:32.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 2.48e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:35.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.34
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.13
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.11
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:47.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.63
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.8e-3

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.16
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.27
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.75
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17707.86
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.67
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.76
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.74
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.30
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.01
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.02
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.84
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.36
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.81
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.18
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.12
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.76
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.07
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.28
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   45.20
p-value of test                       :    0.9967


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.27
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.06
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.33
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.88
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.25
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.18
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.43
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.81
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.55
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.18
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.06
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.26
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.54
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.02
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.28
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.93
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:22.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.95
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -1.53
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:21.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 6.13e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 6.04e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.43
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.12
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.86
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:06.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.25
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9974.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:04:04.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.32
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.22
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.93
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12254.19
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12107.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.25
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000017317

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.82
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999942791

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:02.45

 All tests were passed




Server wird beendet - Lösche Semaphor 104759316.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5656
p-value of test                       :  7.8e-4    *****


-----------------------------------------------
CPU time used                    :  00:03:54.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:38.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:37.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:00.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:02.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:53.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:57.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    2.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:46.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.18
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.90
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:09.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.74
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.94
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:38.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.57
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.27
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.70
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.63
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.20
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1359.01
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:01.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7117.49
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.66
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.29
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:05.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.49
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   90.77
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:33.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5018.92
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:54.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45840
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869840
  j =  1                              :        399908320
  j =  2                              :            45840
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45500
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869500
  j =  1                              :        399909004
  j =  2                              :            45492
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:27.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 7.83e-3
p-value of test                       :    0.9902

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:17.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:44.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 9.78e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:55.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.58e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:33.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:33.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.24
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:48.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.91
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.93
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.90
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.80
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.81
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.73
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.23
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.42
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17461.75
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.13
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.80
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.56
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.03
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.45
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.17
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.54
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.34
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.87
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.55
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.06
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.94
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.18
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.24
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.24
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.90
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.28
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.90
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.22
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.08
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.58
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.08
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.23
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.40
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.70
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.94
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.44
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.24
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.83
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.19
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:22.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.22
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:21.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.95e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 3.52e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   21.96
p-value of test                       :  5.0e-3

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.47
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.87
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.33
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:05.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.47
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9771.12
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:51.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.19
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3941.17
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.13
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11686.65
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11911.33
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.42
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999808181

Normal statistic for number of bits   :   -1.52
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.63
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999986489

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.95
p-value of test                       :    0.03

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    2.61
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:07.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 13  BirthdaySpacings, t = 2         7.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 105742356.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5299
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:55.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:39.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:01.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:02.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:54.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7476
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:57.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:45.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.17
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:10.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.38
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.89
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.40
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.97
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.59
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.05
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.34
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  489.25
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.32
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:03.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7034.62
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.01
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.66
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:06.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.00
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.42
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5143.66
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:57.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46111
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870111
  j =  1                              :        399907782
  j =  2                              :            46103
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908479
  j =  2                              :            45753
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :  3.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9922


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:18.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  9.5e-3

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:03.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:57.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 4.04e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.045
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:32.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.04
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.35
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.12
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:41.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.89
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.35
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.44
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17201.29
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.25
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.90
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.24
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.74
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.10
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.89
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.35
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.26
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.03
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.26
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.47
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.63
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.95
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.78
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.44
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.14
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.01
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5114.37
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.50
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.43
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.45
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.41
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.30
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.36
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.19
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :    1.61
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:23.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.12
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   -1.52
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.61
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.57
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.62
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:05.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.85
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.39
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:40.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.08
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:48.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3995.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.67
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.53
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12067.64
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.47
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000000709

Normal statistic for number of bits   : 5.61e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.39
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999990182

Normal statistic for number of bits   :  -0.078
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:51.87

 All tests were passed




Server wird beendet - Lösche Semaphor 106758164.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9943


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:00.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:43.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4147
p-value of test                       :    0.9981


-----------------------------------------------
CPU time used                    :  00:01:59.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:00.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:09.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:09.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:07.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:10.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:09.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.67
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:39.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.58
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.63
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.90
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.63
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.45
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:09.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7117.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:58.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:12.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.15
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.96
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4814.64
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:30.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:53.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45636
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869636
  j =  1                              :        399908730
  j =  2                              :            45632
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45955
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869955
  j =  1                              :        399908096
  j =  2                              :            45943
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:31.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:06.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:39.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-5
p-value of test                       :    0.9914

Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.31e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:54.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:53.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.01
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.81
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.14
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.33
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:53.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.78
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.84
p-value of test                       :  4.4e-3

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.73e-3
p-value of test                       :    0.9972

Anderson-Darling statistic = A2       :    5.34
p-value of test                       :  2.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16817.66
p-value of test                       :    0.9995    *****



-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.95
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.93
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.18
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.57
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.89
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.55
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.17
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.81
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.58
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.62
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.76
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.56
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  578.83
p-value of test                       :  8.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.49
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.79
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.19
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.34
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.10
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.31
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.99
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.35
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.81
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5206.12
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.59
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.79
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.94
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.48
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.66
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.02
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.39
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:34.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.14
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:21.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.44
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:24.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 5.24e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 6.35e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.67
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.05
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9921

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:24.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.04
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:19.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.35
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9785.49
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.016
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:04:39.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4956.65
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:51.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.64
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.79
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12107.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:32.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11772.75
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:33.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.48
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000086938

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.46
p-value of test                       :  9.3e-3


-----------------------------------------------
Total number of bits:  7999999401

Normal statistic for number of bits   : -4.74e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.98
p-value of test                       :    0.02

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.084
p-value of test                       :    0.47

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:32.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:34.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 73  GCD                             0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 107675668.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5345
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:52.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:39.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4214
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:02.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:04.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:54.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:59.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     854
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    4.86
p-value of test                       :  3.4e-3

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    2.04
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:11.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:40.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.49
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.28
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.81
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:45.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.23
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7193.34
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:46.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:03.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.10
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.29
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:33.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4847.31
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:01.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45432
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869432
  j =  1                              :        399909141
  j =  2                              :            45422
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45833
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869833
  j =  1                              :        399908338
  j =  2                              :            45825
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:28.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:17.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:01.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:53.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:32.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.01e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.56e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.88e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.71
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.72
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.37
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:48.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.17
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.20
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:40.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.74
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17541.21
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.45
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.92
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.69
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.95
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.85
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.33
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.86
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.80
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.56
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.45
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.90
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.05
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.02
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.15
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.23
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.81
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.45
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.94
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.45
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.41
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.64
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  449.31
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.33
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  485.76
p-value of test                       :  1.5e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.72
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.92
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.46
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.66
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.16
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  245.23
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.08
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:25.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.52
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:27.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 7.04e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 8.11e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.82
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.22
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.37
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:05.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.49
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:06.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.48
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:43.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4968.85
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:50.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.59
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.40
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11697.41
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.79
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.25
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000011617

Normal statistic for number of bits   :   0.092
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.51
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999864437

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9990

Tests on the sum of all N observations
Standardized normal statistic         :   0.080
p-value of test                       :    0.47

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:17.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 R (L=10000, r=0)    1.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 109182996.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1242
p-value of test                       :    0.9996    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334362
  j =  1                              :        599997516
  j =  2                              :             1242
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:52.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:40.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:39.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:03.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:03.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:53.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7480
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:59.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.77
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:45.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:12.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:39.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.21
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.71
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.85
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.42
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.49
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.29
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:43.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.15
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:01.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6927.73
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.51
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:04.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.35
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.40
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5140.51
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:11.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45745
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869745
  j =  1                              :        399908510
  j =  2                              :            45745
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45796
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869796
  j =  1                              :        399908413
  j =  2                              :            45786
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:28.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:54.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:32.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 2.85e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.06e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:38.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:39.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.95
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.42
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.65
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.24
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.31
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  161.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17421.13
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.42
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.57
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.78
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.41
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.68
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.36
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.64
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.75
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.94
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.40
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.17
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.45
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.91
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.68
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.01
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.36
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.62
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.69
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.09
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.56
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.45
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.56
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.31
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.19
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.96
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.74
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.74
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.82
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.67
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:23.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.33
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:23.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 2.77e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.83e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.32
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.54
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.73
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:05.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.81
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.68
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:45.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.02
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.36
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.19
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11529.40
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11574.19
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.97
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000049648

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.10
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000074218

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.44
p-value of test                       :    0.08

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:51.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 110133268.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5502
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:54.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4495
p-value of test                       :  8.6e-3


-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:03.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:03.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:54.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:59.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.88
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:14.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.19
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:42.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.18
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.53
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.88
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.92
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.43
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.53
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.02
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:58.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7113.02
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.84e-3
p-value of test                       :    0.9981

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.52
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:03.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.32
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.14
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5021.52
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:58.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46169
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870169
  j =  1                              :        399907666
  j =  2                              :            46161
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45776
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869776
  j =  1                              :        399908450
  j =  2                              :            45772
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:28.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:20.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:02.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:32.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.38e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 3.65e-4
p-value of test                       :  4.9e-3

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 9.33e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.034
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:33.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.11
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.78
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:41.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.01
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.40
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17478.17
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.58
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.98
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.77
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.51
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.60
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.58
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.42
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.50
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.24
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.29
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.13
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.69
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.17
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.68
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.87
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.92
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.72
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.60
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.05
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.96
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.46
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.19
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.79
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.47
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.50
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.24
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.88
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.38
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:23.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.15
p-value of test                       :    0.9944


-----------------------------------------------
Normal statistic for number of jumps  :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.29e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 2.53e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.42e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 6.40e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.76
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.94
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.71
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:05.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.51
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.85
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10063.12
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:43.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.52
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.00
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11475.87
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:29.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.84
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000012889

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.65
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999982409

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :  -0.042
p-value of test                       :    0.52

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:09.37

 All tests were passed




Server wird beendet - Lösche Semaphor 111116308.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:54.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7476
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:00.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.97
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     642
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:13.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.98
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:41.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.35
p-value of test                       :    0.9998    *****

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.74
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.76
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.68
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  493.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1496.28
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7203.63
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:02.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.63
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.11
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5035.07
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45639
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869639
  j =  1                              :        399908725
  j =  2                              :            45633
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45953
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869953
  j =  1                              :        399908097
  j =  2                              :            45947
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:28.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:18.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:59.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 7.24e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.86e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.15
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.77
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.95
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.80
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.15
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.49
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17577.11
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.15
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.00
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.96
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.06
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.12
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.00
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.42
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.67
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.07
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.86
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.54
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.74
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.59
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.42
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.46
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  435.32
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.79
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.46
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.58
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.77
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.73
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.04
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.15
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.32
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.95
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.60
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.70
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.04
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.87
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.91
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:20.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.46e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 6.90e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.95
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.12
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.21
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.31
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9900.86
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.052
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:40.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4740.71
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.25
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.52
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3961.13
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11851.41
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.72
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999960377

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.78
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999950750

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:26.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 27  SimpPoker, r = 27               0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 112099348.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:43.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:09.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:08.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:03.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:07.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:51.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    2.17
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     546
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9925

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.44
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:17.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:43.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.57
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.66
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.84
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.33
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.11
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.90
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.42
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.23
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:58.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.25
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:16.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7114.08
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.96
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.64
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:17.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.63
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.25
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5146.07
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:59.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46097
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870097
  j =  1                              :        399907809
  j =  2                              :            46091
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46004
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870004
  j =  1                              :        399908001
  j =  2                              :            45986
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:32.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:20.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:38.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.71e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:46.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:44.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.49
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.03
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.74
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.71
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:52.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.70
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 6.61e-4
p-value of test                       :    0.9993    *****

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.82
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.04
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17384.70
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.29
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.23
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.00
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.53
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.24
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.71
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.64
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.50
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.50
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.93
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.59
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.82
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.92
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.66
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.70
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.80
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.96
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.32
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.23
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  246.64
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.34
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.25
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.15
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.63
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.84
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.41
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -1.65
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:26.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.87
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :  -0.095
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:23.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 5.09e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.68e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.62
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.68
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.9e-3

Anderson-Darling statistic = A2       :    3.78
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  248.15
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:06.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:06.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10035.74
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9959.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:04:25.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.30
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:55.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.72
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.96
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:35.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11735.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:36.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.26
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999903485

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.63
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000006691

Normal statistic for number of bits   :   0.053
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.029
p-value of test                       :    0.49

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.5e-3

Kolmogorov-Smirnov- statistic = D-    : 8.15e-3
p-value of test                       :    0.9912

Anderson-Darling statistic = A2       :    5.46
p-value of test                       :  1.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -3.27
p-value of test                       :    0.9995    *****

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:53.48
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 106  AutoCor, d=3, r=27              0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 113016852.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5525
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:56.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4178
p-value of test                       :    0.9922


-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:10.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:10.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:07.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:11.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    2.46
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:14.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:41.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.16
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.92
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.27
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.01
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.49
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:59.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1537.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:09.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7145.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.79
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.55
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:20.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.22
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.59
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:44.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5109.16
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:00.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45477
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869477
  j =  1                              :        399909050
  j =  2                              :            45469
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45776
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869776
  j =  1                              :        399908450
  j =  2                              :            45772
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:31.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:20.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:08.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 2.61e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.93e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.36e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.047
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.50
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.43
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.23
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.55
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.64
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.66
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:52.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.42
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17455.78
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.48
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.23
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.24
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.57
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.07
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.37
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.47
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.89
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.65
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.86
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.99
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.43
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.29
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.97
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.72
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.32
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.96
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.25
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.93
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.32
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.91
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  242.80
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.80
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.43
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.75
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.66
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.53
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.87
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    2.61
p-value of test                       :  4.5e-3



-----------------------------------------------
CPU time used                    :  00:02:26.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.99
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -1.45
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:24.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.27e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :  8.2e-3

Anderson-Darling statistic = A2       :    4.57
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.59e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.58
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.58
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  154.92
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:02:04.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.00
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:04.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.79
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:04:34.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:57.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4771.06
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.92
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12047.00
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:36.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11776.95
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:39.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.36
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999831971

Normal statistic for number of bits   :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.95
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000025843

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.04e-3
p-value of test                       :    0.9902

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    2.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:24.43

 All tests were passed




Server wird beendet - Lösche Semaphor 114196500.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5588
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:53.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:41.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:59.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:09.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:09.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:07.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:14.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    3.67
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.95
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:14.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    2.00
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:42.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.97
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.06
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.05
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.58
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.88
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:34.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.33
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1323.76
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:11.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6901.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:55.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.82
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.35
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:16.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.71
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  148.79
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4975.98
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:08.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45699
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869699
  j =  1                              :        399908607
  j =  2                              :            45689
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45787
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869787
  j =  1                              :        399908432
  j =  2                              :            45775
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:31.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:10.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 8.79e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 4.87e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.09
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.73
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.36
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.44
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:57.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.12
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.86
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.13
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17470.14
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.50
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.66
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.07
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.13
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.53
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.87
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.20
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.50
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.80
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.99
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.79
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.11
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.20
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.02
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.95
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  196.37
p-value of test                       :  5.5e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.67
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.46
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.74
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4859.87
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.35
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.26
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.95
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.09
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.52
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.05
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.41
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.55
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:21.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.99
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:21.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 4.50e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.44e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.41
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:41.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.80
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.21
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:29.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.75
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:29.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10044.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9810.64
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:04:35.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5071.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:52.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.67
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12069.21
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11879.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:38.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.68
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999912998

Normal statistic for number of bits   :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.64
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999996134

Normal statistic for number of bits   :  -0.031
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    2.53
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:38.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:06.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 R (L=1000, r=20)    5.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 115343380.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5218
p-value of test                       :    0.9972


-----------------------------------------------
CPU time used                    :  00:03:55.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:06.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:06.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:56.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:02.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9942

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:15.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:43.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.63
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.28
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.68
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.50
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.54
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.44
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.35
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.88
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:43.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.75
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6856.49
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.92
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.59
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4946.00
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:02.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46276
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870276
  j =  1                              :        399907450
  j =  2                              :            46272
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45652
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869652
  j =  1                              :        399908698
  j =  2                              :            45648
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:27.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:17.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:55.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 5.17e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:36.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:37.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.36
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.66
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.24
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.48
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:37.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.30
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.87
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17235.73
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.06
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.48
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.20
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.84
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.30
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.25
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.07
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.92
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.16
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.37
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.79
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.13
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.32
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.00
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.46
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.52
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.52
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.63
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.97
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.63
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.62
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.19
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.89
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.40
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.90
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4849.43
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.55
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.38
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.40
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:20.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.51
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -0.63
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:20.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.09e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.58
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.34
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   41.00
p-value of test                       :  2.3e-3



-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.49
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:05.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.79
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:05.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10245.06
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10224.67
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:35.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4671.44
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3968.27
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.09
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.17
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11750.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.18
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999915470

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.62
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999908612

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.06

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:50.84

 All tests were passed




Server wird beendet - Lösche Semaphor 116752404.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5504
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:57.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:05.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:05.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:55.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:00.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    2.46
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:05.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9913

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:17.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:45.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.84
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.53
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.18
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.92
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.67
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.03
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.69
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.83
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1532.09
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6916.60
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:41.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.18
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.62
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:04.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.55
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.83
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:33.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4885.87
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:02.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45751
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869751
  j =  1                              :        399908499
  j =  2                              :            45749
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46078
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870078
  j =  1                              :        399907847
  j =  2                              :            46072
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:31.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 8.86e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    5.05
p-value of test                       :  2.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  1.1e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:26.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:53.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:07.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:54.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.12e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : 2.98e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:40.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:38.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.83
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:47.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.52
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.50
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.29
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:48.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.20
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.57
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:37.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   64.42
p-value of test                       :  8.5e-3

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.38
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17239.22
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.83
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.61
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.66
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.39
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.43
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   16.15
p-value of test                       :    0.9982


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.64
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.59
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    8.26
p-value of test                       :    0.9988


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.87
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.77
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.48
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.39
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.58
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.09
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.73
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.43
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.97
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.48
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.45
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.05
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.43
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.51
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.10
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.27
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.50
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.69
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.32
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.88
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    1.71
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:23.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.87
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:22.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-3
p-value of test                       :    0.9978

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.67
p-value of test                       :  3.8e-3

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.37e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.52
p-value of test                       :    0.9923

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.44
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.86
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:03.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.48
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:02.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9869.12
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10127.16
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.016
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:04:24.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4790.97
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.59
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4048.92
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.30
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11944.93
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   31.52
p-value of test                       :    0.9938


-----------------------------------------------
Total number of bits:  8000042568

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.33
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000166432

Normal statistic for number of bits   :    1.32
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:15.05

 All tests were passed




Server wird beendet - Lösche Semaphor 117637140.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:56.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:41.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:05.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:56.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:00.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.36
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.36
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:14.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:42.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.97
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.21
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.70
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.05
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  473.59
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.36
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7084.47
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:46.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.57
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:03.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.13
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.33
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:33.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4871.43
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:02.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45775
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869775
  j =  1                              :        399908454
  j =  2                              :            45767
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45946
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869946
  j =  1                              :        399908112
  j =  2                              :            45938
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:29.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:20.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9981

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:59.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.29e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.12e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:44.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.33
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.33
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.12
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.92
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:37.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.97
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.99
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.89
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.45
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17432.86
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.58
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.82
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.88
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.65
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   39.31
p-value of test                       :  1.6e-3


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.57
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.49
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.71
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.28
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.91
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.47
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.37
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.65
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.28
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.39
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.79
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.05
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.16
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.27
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.45
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.80
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.00
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.74
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.05
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.25
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.02
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.35
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.38
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.47
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.52
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.99
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:22.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.77
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :  -0.091
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:20.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    2.61
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 3.55e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 8.77e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.00
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.39
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:05.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 2.96e-3
p-value of test                       :    0.9970

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9767.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9917.06
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -3.00
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:37.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.86
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.64
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:51.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4351.22
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4008.62
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11506.76
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11780.89
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.85
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999948743

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.04
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000103819

Normal statistic for number of bits   :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:29.97

 All tests were passed




Server wird beendet - Lösche Semaphor 118652948.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1247
p-value of test                       :    0.9993    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334367
  j =  1                              :        599997506
  j =  2                              :             1247
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1240
p-value of test                       :    0.9997    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334360
  j =  1                              :        599997520
  j =  2                              :             1240
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5523
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:56.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:04.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:05.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:55.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:02.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.36
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     950
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    3.80
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:13.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:43.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.75
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.09
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.94
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.64
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.96
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.16
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1351.53
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:02.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7118.48
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.25
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.45
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:04.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.40
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.48
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:32.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5097.54
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46088
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870088
  j =  1                              :        399907826
  j =  2                              :            46084
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46135
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870135
  j =  1                              :        399907734
  j =  2                              :            46127
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  2.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9925


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:27.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:18.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:59.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.50e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.61e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:34.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:34.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.90
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.26
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.99
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.98
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.34
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17513.74
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.06
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.48
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.65
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.77
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.89
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.03
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.12
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.39
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.55
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.93
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.64
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.57
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.41
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.07
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.06
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.37
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.55
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.50
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.46
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.03
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.08
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4852.30
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.83
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.26
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.58
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.56
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.16
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.91
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.98
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.52
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:21.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.09
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :   -1.52
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:21.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9945

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.39e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.92e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.53
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.55
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:02.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.62
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:03.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10167.72
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9836.69
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:37.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.85
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4794.74
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3969.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4254.57
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11679.28
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11637.32
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.70
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999942368

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.98
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000073771

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :  -0.031
p-value of test                       :    0.51

Sample variance                       :    1.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:46.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  7  CollisionOver, t = 7            0.9993 
  9  CollisionOver, t = 14           0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 119603220.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:56.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7120
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:05.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:56.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:01.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    2.11
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:16.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     181
p-value of test                       :  7.6e-3

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.78
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.34
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.66
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.58
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.01
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.61
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.83
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1501.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:59.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7193.96
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:42.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.76
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:03.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.80
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.20
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:33.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5017.27
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:54.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46030
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870030
  j =  1                              :        399907942
  j =  2                              :            46026
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45497
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869497
  j =  1                              :        399909009
  j =  2                              :            45491
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:28.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:59.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:38.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.26e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.93e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:35.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:47.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.19
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.79
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.25
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.95
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.95
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.78
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.27
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17315.21
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.89
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.46
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.23
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.03
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.69
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.68
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.72
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.22
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.25
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.25
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.69
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.68
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.89
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.02
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.31
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.37
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.07
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.50
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.14
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.00
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.86
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.23
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  430.07
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.56
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.36
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.69
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.17
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.97
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.58
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:23.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.01
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:22.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 4.99e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.76e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 5.80e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.80
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.01
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.41
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:02.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.39
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:04.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9899.74
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.76
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:39.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4984.40
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4749.91
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4268.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.58
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11644.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.71
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.76
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999833534

Normal statistic for number of bits   :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.19
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000143128

Normal statistic for number of bits   :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    2.45
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:08.10

 All tests were passed




Server wird beendet - Lösche Semaphor 120553492.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5340
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:55.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:41.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:05.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:05.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:55.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:00.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.87
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.75
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.66
p-value of test                       :  1.5e-3

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:16.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    2.14
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:44.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.32
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.82
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.59
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.06
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.23
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1536.64
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6936.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.3e-3

Anderson-Darling statistic = A2       :    3.80
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:03.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.38
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.64
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:33.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4946.13
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:00.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46157
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870157
  j =  1                              :        399907690
  j =  2                              :            46149
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45980
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869980
  j =  1                              :        399908046
  j =  2                              :            45968
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:28.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:35.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.26e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:44.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.77
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:48.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.41
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.63
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.26
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.76
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.16
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.88
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.84
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17330.04
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.09
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   45.02
p-value of test                       :  8.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.17
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.57
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.81
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.63
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.06
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.36
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.59
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.89
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.65
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.68
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.75
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.11
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  568.52
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.42
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.07
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.83
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.07
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.53
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.23
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  250.42
p-value of test                       :  8.9e-3


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.32
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5103.49
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.88
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.02
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:13.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.24
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:11.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.98e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 3.81e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:40.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.84
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.38
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:55.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9937.41
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.54
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:19.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:37.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.90
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11633.17
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.39
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.98
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000046723

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.41
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000051478

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:58:24.10

 All tests were passed




Server wird beendet - Lösche Semaphor 121569300.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5509
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:35.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:54.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:03.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:03.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:58.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:02.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     334
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:07.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:37.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.05
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.20
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.09
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.83
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.41
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  267.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  355.87
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1370.18
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7072.97
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:54.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.33
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.74
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:14.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.10
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.70
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:10.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5060.34
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:35.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:43.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45637
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869637
  j =  1                              :        399908728
  j =  2                              :            45633
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45468
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869468
  j =  1                              :        399909066
  j =  2                              :            45464
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:30.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:16.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :  2.0e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.72
p-value of test                       :  4.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9953


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:44.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:54.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.25e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.088
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:47.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.86
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.25
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.68
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.84
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.08
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.04
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.50
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.05
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.34
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.89e-3
p-value of test                       :    0.9960

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17063.11
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.16
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.18
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.33
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.89
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.76
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.98
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.74
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.50
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.58
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.12
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.72
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.06
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.06
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.74
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.78
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.27
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.54
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.70
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.68
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.79
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.16
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.85
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4811.15
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.93
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  255.99
p-value of test                       :  4.6e-3


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.93
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.75
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.34
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.53
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.05
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.13
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:24.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.72
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:26.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.90e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 6.11e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.24
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.68
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.24
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:08.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.49
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:06.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.51
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10143.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.097
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:04:22.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:53.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.72
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4350.77
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.24
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:34.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:35.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.77
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999984617

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.57
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000138652

Normal statistic for number of bits   :    1.10
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.11
p-value of test                       :    0.98

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:11.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:19:21.87

 All tests were passed




Server wird beendet - Lösche Semaphor 102268949.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:26.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1250
p-value of test                       :    0.9991    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334370
  j =  1                              :        599997500
  j =  2                              :             1250
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5433
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:48.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4218
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:38.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:37.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:02.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:02.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:51.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:01.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     944
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:14.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:42.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.18
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.22
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.23
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  275.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.92
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.70
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7139.09
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.28
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:05.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.69
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.28
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:33.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5156.32
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:58.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45904
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869904
  j =  1                              :        399908195
  j =  2                              :            45898
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46159
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870159
  j =  1                              :        399907687
  j =  2                              :            46149
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:23.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:14.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:54.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:33.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:31.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.62
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.64
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.39
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.96
p-value of test                       :    0.9900

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.40
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.99
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.89
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.47
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17222.91
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.20
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.16
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.10
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.52
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.29
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.15
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.35
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.34
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.90
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.33
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.48
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.10
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.63
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.78
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.63
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.41
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.79
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.70
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  172.00
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.59
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.25
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4887.80
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.15
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.87
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.13
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.53
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.84
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.98
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.83
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.14
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.99
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:23.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 5.10e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.22e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.36
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.97
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.36
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:07.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.07
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:07.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.96
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.015
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.054
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:43.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.58
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:51.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.88
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.48
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12037.30
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11980.11
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.88
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000001057

Normal statistic for number of bits   : 8.36e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.76
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000005653

Normal statistic for number of bits   :   0.045
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.6e-3

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    2.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:53.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  8  CollisionOver, t = 7            0.9991 
 ----------------------------------------------
 All other tests were passed




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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5504
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:48.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:38.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:37.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:55.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:02.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:02.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:53.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:02.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    2.40
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     946
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    4.72
p-value of test                       :  3.9e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     675
p-value of test                       :  1.4e-3

Stat. AD (mNP2)                       :    2.82
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    3.93
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:13.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    2.12
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:41.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.54
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.42
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   25.76
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.97
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.48
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.02
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1367.97
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:59.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7093.53
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.43
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.59
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:01.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.83
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.36
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:33.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5233.64
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:59.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45959
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869959
  j =  1                              :        399908085
  j =  2                              :            45953
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46060
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870060
  j =  1                              :        399907882
  j =  2                              :            46056
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:26.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:17.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 4.64e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:31.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.75
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.56
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.76
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.70
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.01
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.81
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17415.25
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.28
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.67
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.60
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.92
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   69.41
p-value of test                       :  6.9e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.15
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.00
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.87
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.03
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.49
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.03
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.42
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.84
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.38
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.92
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.32
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.81
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.77
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.78
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.56
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.12
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.00
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.92
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.96
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.55
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.01
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.23
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    0.16
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:24.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.20
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:23.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.05e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.21
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.03
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.12
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:06.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.66
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:06.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9896.35
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:44.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.95
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.16
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:50.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.20
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.38
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.97
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.29
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000102187

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.02
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999916865

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   0.059
p-value of test                       :    0.48

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.05

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:29.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 30  CouponCollector, r = 0          0.9996 
 75  RandomWalk1 H (L=50, r=25)      6.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 104300565.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:48.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:38.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:37.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:01.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:02.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:52.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:00.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.13
p-value of test                       :    0.9995    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9949

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    3.59
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:13.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    2.76
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     124
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:47.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.48
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.43
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.31
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  492.70
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:46.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7020.46
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.47
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:06.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.42
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.27
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:33.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5037.02
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45964
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869964
  j =  1                              :        399908073
  j =  2                              :            45962
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46302
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870302
  j =  1                              :        399907397
  j =  2                              :            46300
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:26.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.17e-3
p-value of test                       :    0.9940

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:16.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.62e-3
p-value of test                       :    0.9950

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 6.20e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:32.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:48.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.80
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.69
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.48
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:37.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.00
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.90
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.38
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17730.91
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.17
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.41
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.92
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.65
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.95
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.71
p-value of test                       :    0.9934


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.41
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.55
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.20
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.23
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.06
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.15
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.28
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.79
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.28
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.79
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.45
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.02
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.78
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.22
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.25
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.53
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.59
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.31
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.45
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.64
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.30
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.32
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.02
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :   -1.67
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:21.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    2.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 2.32e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.83
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.16
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.89
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:06.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.01
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9913.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10158.93
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.67
p-value of test                       :    0.9962

-----------------------------------------------
CPU time used                    :  00:03:42.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.23
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:50.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.91
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4262.08
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12168.88
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11913.10
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.11
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999972707

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.11
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000078940

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:51.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs NP, t = 5            0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 105250837.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:41.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5477
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:48.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:38.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:38.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:55.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:02.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:01.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:51.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:59.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     950
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:12.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:42.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.38
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.98
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.68
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.39
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.23
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:44.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1378.63
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:00.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7172.13
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:01.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.46
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.50
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:34.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5026.68
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:04.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45504
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869504
  j =  1                              :        399908994
  j =  2                              :            45500
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45977
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869977
  j =  1                              :        399908046
  j =  2                              :            45977
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:26.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 8.53e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:17.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:32.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.63e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.21e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.027
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.41
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:48.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.01
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.48
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.77
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17587.89
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.90
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.59
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.45
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.31
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.07
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.87
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.64
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.58
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.67
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.32
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.80
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.11
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.81
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.49
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.53
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.80
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.43
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.14
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.02
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.77
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.88
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4898.93
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.04
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.96
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.29
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.13
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.00
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.45
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.53
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.04
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:22.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.91
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.76e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.92
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.92
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.77
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.96
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10021.36
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:42.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.56
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4770.18
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:49.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4307.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.14
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11599.09
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11720.94
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.85
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999841766

Normal statistic for number of bits   :   -1.25
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.16
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000106525

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.5e-3

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:46.29

 All tests were passed




Server wird beendet - Lösche Semaphor 106135573.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5503
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:49.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:39.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:57.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:03.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7472
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:01.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:52.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:59.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     552
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.55
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    2.26
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:12.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:35.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.13
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.89
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.43
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.17
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.18
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.25
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.95
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1387.72
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6999.97
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:41.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.48
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.15
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:01.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.89
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.98
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4955.24
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:58.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908186
  j =  2                              :            45901
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45740
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869740
  j =  1                              :        399908523
  j =  2                              :            45734
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:27.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:18.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:01.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:55.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.074
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:33.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.19
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.45
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.31
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.98
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17649.67
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.74
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.18
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.68
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.52
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.04
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.29
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.87
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.85
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.21
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.79
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.61
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.54
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.15
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.34
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.61
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.73
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.85
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.45
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.96
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.05
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.29
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5108.25
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  430.50
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.97
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.14
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.19
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.56
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.27
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.68
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :    2.15
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:24.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.62
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    2.38
p-value of test                       :  8.7e-3



-----------------------------------------------
CPU time used                    :  00:02:23.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 3.96e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.02e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.11
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.06
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:05.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:07.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10024.63
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9759.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.098
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:40.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.34
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:49.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.62
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:50.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.67
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11955.47
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.58
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.92
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000129691

Normal statistic for number of bits   :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.24
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999959399

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.92

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:33.30

 All tests were passed




Server wird beendet - Lösche Semaphor 107085845.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:49.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:38.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7111
p-value of test                       :    0.9924


-----------------------------------------------
CPU time used                    :  00:03:02.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:02.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:51.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:59.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.29
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.68
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:12.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.95
p-value of test                       :  3.4e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    2.18
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:38.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.10
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.20
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.13
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.09
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.61
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.90
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:59.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6899.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.54
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.71
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:03.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   88.67
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4917.09
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:10.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46295
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870295
  j =  1                              :        399907412
  j =  2                              :            46291
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45880
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869880
  j =  1                              :        399908241
  j =  2                              :            45878
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:27.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:19.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.31e-3
p-value of test                       :    0.9929

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  9.3e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:55.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:32.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.98e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.041
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:37.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:38.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.46
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.41
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.38
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:48.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.14
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.26
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:38.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.42
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.23
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.12
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17726.72
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.72
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.43
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.01
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.06
p-value of test                       :    0.9975


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.06
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.31
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.98
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.79
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.81
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.03
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.97
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.00
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.91
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.66
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.46
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.70
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  432.62
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.71
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.97
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.98
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.82
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4889.87
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.98
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  255.63
p-value of test                       :  4.8e-3


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.38
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.17
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.16
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.73
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.96
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.76
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.60
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:22.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 5.45e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.73e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.16
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.63
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.93
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:06.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.26
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9913.15
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:39.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.56
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.83
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4232.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12020.48
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11979.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.47
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999908894

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.99
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000070864

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.31e-3
p-value of test                       :    0.9944

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.38
p-value of test                       :  8.6e-3

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:00.39

 All tests were passed




Server wird beendet - Lösche Semaphor 107970581.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:50.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:38.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:05.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:05.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:55.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:59.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.31
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    2.17
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     548
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    2.99
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.21
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    2.45
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:13.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.95
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:41.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.03
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.72
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.39
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.10
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.91
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.05
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.61
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.42
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.70
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:05.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6773.58
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.10
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.89
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:09.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.06
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.43
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5162.04
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:00.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45671
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869671
  j =  1                              :        399908662
  j =  2                              :            45663
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45933
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869933
  j =  1                              :        399908141
  j =  2                              :            45919
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:30.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:20.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:04.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:22.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   99.21
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.90
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.10
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.81
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.09
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.58
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.45
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17255.25
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.19
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.57
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.51
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.23
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.09
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.05
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.58
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.24
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.32
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.41
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.91
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.74
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.00
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.03
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.99
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.61
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.57
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.96
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.90
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.21
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.44
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.46
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.01
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.07
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.39
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.94
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.05
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.81
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.24
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:24.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.62
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.83e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.47e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.66
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.96
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.60
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:07.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:07.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.73
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9909.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.24
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:04:17.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4961.54
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:53.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.37
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:54.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.29
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11781.10
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.75
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.28
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000042523

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.84
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999865814

Normal statistic for number of bits   :   -1.06
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.43

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:23.94

 All tests were passed




Server wird beendet - Lösche Semaphor 108888085.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:50.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:03.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:03.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:53.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:59.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.45
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    4.39
p-value of test                       :  5.7e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     551
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:13.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    2.63
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:43.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.42
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.55
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.43
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.72
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.50
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1409.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7018.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.33
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.42
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:04.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.02
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.23
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4803.50
p-value of test                       :    0.9913


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:56.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45954
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869954
  j =  1                              :        399908096
  j =  2                              :            45946
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46421
p-value of test                       :  5.8e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870421
  j =  1                              :        399907162
  j =  2                              :            46413
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:28.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:20.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:47.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:32.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.95e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 3.70e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.63
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:47.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.28
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.16
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.08
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.90
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.01
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.15
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.52
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   91.92
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17670.50
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.91
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.35
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.26
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.15
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.31
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.54
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.98
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.92
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.31
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.42
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.49
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.61
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.75
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.15
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.23
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.15
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.96
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.78
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.85
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.21
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.77
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.65
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.03
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.05
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.60
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.65
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.02
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5132.68
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.37
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.14
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.80
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.05
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.84e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 3.20e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.48
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.11
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 5.85e-3
p-value of test                       :    0.9938

Anderson-Darling statistic = A2       :    4.76
p-value of test                       :  4.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  145.67
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.77
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:07.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10171.00
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10182.49
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.100
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:43.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.20
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.29
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:50.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4252.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4309.67
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11999.20
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11740.83
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.04
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999917177

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.62
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000018055

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :  -0.019
p-value of test                       :    0.51

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:20.84

 All tests were passed




Server wird beendet - Lösche Semaphor 110034965.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5341
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:55.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:43.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4191
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:01.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:11.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:10.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:08.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:11.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:13.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.02
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:41.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.98
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.29
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.51
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.74
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.49
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.52
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:09.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7008.21
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   48.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.38
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:10.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.28
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.79
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:40.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4959.82
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45959
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869959
  j =  1                              :        399908088
  j =  2                              :            45947
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45419
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869419
  j =  1                              :        399909162
  j =  2                              :            45419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:29.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:23.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:56.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.18e-4
p-value of test                       :    0.9994    *****

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.87
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:14.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:58.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.92e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:53.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.29
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.92
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.12
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.11
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.43
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.78
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:52.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.51
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.45
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17336.99
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.11
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.43
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.63
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.76
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.39
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.58
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.17
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.20
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.44
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.89
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.17
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  411.65
p-value of test                       :    0.9984


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.84
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.14
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.64
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.63
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.29
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.30
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.34
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.50
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.54
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.78
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.66
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.26
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.00
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.70
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.18
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.36
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.60
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.08
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :    1.83
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:23.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.35
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:23.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 3.41e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 8.01e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.79
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.21
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:35.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.84
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:08.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.18
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:07.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  1.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.62
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9686.39
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.21
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:04:34.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5098.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:52.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.58
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.01
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.98
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11958.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.86
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999937088

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.77
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999995291

Normal statistic for number of bits   :  -0.037
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.79
p-value of test                       :    0.04

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.64e-3
p-value of test                       :    0.9952

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.60
p-value of test                       :  4.7e-3

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:54.64

 All tests were passed




Server wird beendet - Lösche Semaphor 111050773.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5478
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:55.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:41.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:59.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:10.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:11.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:06.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:11.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:13.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.05
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:42.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.38
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.94
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.07
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.73
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.20
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.65
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  273.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  384.98
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:56.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:05.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7065.89
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:57.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.42
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.49
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:20.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.46
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4853.72
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:55.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46280
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870280
  j =  1                              :        399907441
  j =  2                              :            46278
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45812
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869812
  j =  1                              :        399908377
  j =  2                              :            45810
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:33.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:21.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:51.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:10.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:37.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 4.00e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.089
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.08
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.51
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.84
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.70
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.88
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17380.36
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.78
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.73
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.61
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.70
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.53
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.90
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.28
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.23
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.39
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.82
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.35
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.49
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.11
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.96
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.66
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.16
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.71
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.65
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.55
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.45
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4893.68
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.66
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  449.37
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.26
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4811.53
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  433.16
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.66
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.29
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:24.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.02
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -1.54
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 5.22e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.21e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.62
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.25
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.23
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:04.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.94
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:05.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.67
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10105.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:04:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:57.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4768.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.13
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.47
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11851.85
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:36.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11922.81
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.57
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999982931

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.49
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999804191

Normal statistic for number of bits   :   -1.55
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.60
p-value of test                       :    0.94

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:03.77

 All tests were passed




Server wird beendet - Lösche Semaphor 112427029.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5472
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:53.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:39.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:05.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:05.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:55.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7505
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:01.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.87
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     959
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.24
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.09
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:12.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:42.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.90
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.26
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.91
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.04
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.03
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:43.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6887.23
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:41.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:04.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.44
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.19
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4979.63
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:59.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45760
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869760
  j =  1                              :        399908482
  j =  2                              :            45756
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46090
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870090
  j =  1                              :        399907824
  j =  2                              :            46082
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:27.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:18.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.38
p-value of test                       :  5.9e-3


-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:53.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.24e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.14
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.06
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.22
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:49.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   61.87
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.32
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.71
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.15
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.06
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.23
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17367.58
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.72
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.94
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.67
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.21
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.25
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.52
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.14
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.07
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.08
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.82
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.91
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.26
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.08
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.20
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.89
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.88
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.05
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.44
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.82
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.79
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.74
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.47
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.90
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.88
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.61
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.53
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.59
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  249.78
p-value of test                       :  9.6e-3


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.66
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.59
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.31e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 8.46e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 4.95e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.12
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.59
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.12
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.45
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:05.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.63
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.06
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:40.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4771.98
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:46.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4957.63
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.95
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.47
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11862.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.93
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000012637

Normal statistic for number of bits   :   0.100
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.42
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999969062

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    4.16
p-value of test                       :  7.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.24
p-value of test                       :    0.99

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:47.12

 All tests were passed




Server wird beendet - Lösche Semaphor 113573909.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5387
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:51.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:39.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4461
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:06.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:07.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7140
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:01.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:04.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.55
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     958
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    3.13
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     659
p-value of test                       :  9.2e-3

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:13.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.66
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.35
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.30
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.96
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.98
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.77
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.13
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.45
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.33
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.73
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:03.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7018.14
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:51.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.68
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.38
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:10.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.78
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.93
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:37.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4853.28
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:59.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45828
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869828
  j =  1                              :        399908348
  j =  2                              :            45820
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45962
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869962
  j =  1                              :        399908081
  j =  2                              :            45952
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:29.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:02.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:55.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  8.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.23e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.61
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.071
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:45.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.55
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.08
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.41
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.00
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.63
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.76
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.23
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.75
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.09
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17310.48
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.50
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.01
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.13
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.41
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.93
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.06
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.15
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.85
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.03
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.31
p-value of test                       :    0.9954


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.23
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.05
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.27
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.62
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.97
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.18
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  416.95
p-value of test                       :    0.9972


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.23
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.73
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.20
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.64
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4892.65
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.97
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.55
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.64
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.18
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.28
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.55
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.21
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.20
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.79
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:23.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.09e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 6.21e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 5.78e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.96
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.95
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.23
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.95
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:04.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10023.71
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9880.48
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:04:12.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4695.86
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:52.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:53.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.27
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11625.06
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11913.45
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.48
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999953861

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.57
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000036208

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:20.70

 All tests were passed




Server wird beendet - Lösche Semaphor 114589717.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5482
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:52.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:05.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:05.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:55.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:01.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:12.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:42.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.96
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.68
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.38
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.64
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.43
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.18
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.83
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.24
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:43.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.56
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7124.83
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.99
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.90
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:02.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.90
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.15
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4987.35
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:05.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45881
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869881
  j =  1                              :        399908242
  j =  2                              :            45873
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869892
  j =  1                              :        399908221
  j =  2                              :            45882
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:28.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:18.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9974

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 8.20e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:59.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:55.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 8.42e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:32.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:36.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.64
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.14
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.41
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.03
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.84
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.14
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:39.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.06
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.38
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.56
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.11
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17292.91
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.01
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.48
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.72
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.35
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.83
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.24
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.67
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.43
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.03
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.17
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.31
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.52
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.20
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.23
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.50
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.04
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.10
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.01
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.88
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.15
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.03
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  452.50
p-value of test                       :  9.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4838.49
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.39
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.69
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.16
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.28
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.06
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.02
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -1.95
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:23.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.74
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:23.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 3.53e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 3.73e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.89
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.06
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:07.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.48
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:04.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9863.93
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
p-value of test                       :    0.9936

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10327.23
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4968.14
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:50.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4205.80
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4233.35
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.48
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11708.45
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.06
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999932846

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.16
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999997613

Normal statistic for number of bits   :  -0.019
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:14.79

 All tests were passed




Server wird beendet - Lösche Semaphor 115638293.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5500
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:54.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:39.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:58.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7496
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:06.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:06.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:56.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:01.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    3.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9913


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:15.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:42.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.32
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.43
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.56
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.75
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  191.36
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.69
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.31
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:01.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7045.81
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.64
p-value of test                       :  7.8e-3

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.77
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:03.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.13
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.71
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:33.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5154.41
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:54.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46032
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870032
  j =  1                              :        399907938
  j =  2                              :            46028
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45969
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869969
  j =  1                              :        399908066
  j =  2                              :            45961
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:28.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:58.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 9.90e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.39e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.08
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.61
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.74
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.15
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    4.63
p-value of test                       :  4.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   69.19
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.023
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.88
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17598.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:52.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.89
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.06
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.54
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.97
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.60
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.31
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.06
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.02
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.69
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.32
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.79
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.65
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.57
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.31
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.03
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.23
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.71
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.20
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.65
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4875.93
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.05
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.07
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.09
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  313.46
p-value of test                       :    0.9965


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.61
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.02
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.81
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.64
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -1.58
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.56
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:21.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.93

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.67e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.76e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.49e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.45
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.67
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:04.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.42
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:05.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10009.44
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9844.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:36.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4784.28
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4732.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.77
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.23
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11687.14
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.58
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.71
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000037258

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.90
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000071683

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.072
p-value of test                       :    0.53

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :  -0.040
p-value of test                       :    0.52

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:28.82
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 68  MatrixRank, L=1000, r=0         0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 116523029.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:52.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:59.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:08.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:08.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:01.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:02.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.95
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.15
p-value of test                       :    0.9986

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:13.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    2.19
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:43.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.29
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.43
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.53
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.14
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.96
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.02
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:05.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7300.60
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.89
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:19.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.93
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.17
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5082.00
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:58.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45893
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869893
  j =  1                              :        399908217
  j =  2                              :            45887
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45914
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869914
  j =  1                              :        399908177
  j =  2                              :            45904
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:28.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :  4.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:17.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 8.79e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.027
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.89
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.29
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:44.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.25
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.04
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.26
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17194.93
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:52.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.96
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.51
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.66
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.84
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.12
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.92
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.95
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.39
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.25
p-value of test                       :    0.9913


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.57
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.05
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  444.62
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.99
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   36.58
p-value of test                       : 1 -  7.9e-5    *****


-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.71
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.72
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.51
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.05
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.63
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.95
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.27
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.22
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.50
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.06
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:34.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.32
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.03
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.07
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.01
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.91
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.52
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:22.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.76
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:22.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.99e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.09
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.16
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.76
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:03.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:04.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.51
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9870.08
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:04:06.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5019.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:50.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4768.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:52.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3947.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3971.49
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11770.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11459.60
p-value of test                       :    0.9917

-----------------------------------------------
CPU time used                    :  00:01:29.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.42
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000089617

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.39
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000135820

Normal statistic for number of bits   :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :  -0.018
p-value of test                       :    0.51

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:27.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 C (L=1000, r=0)    1 -  7.9e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 117538837.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:48.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:27.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5541
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:54.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:06.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:06.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:55.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:00.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    2.82
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    3.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     336
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:13.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.18
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.12
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.83
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.52
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.00
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.36
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.28
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.19
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.64
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.55
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.15
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6959.69
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.36
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.19
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:25.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.40
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.07
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:33.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5065.69
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:00.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45521
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869521
  j =  1                              :        399908962
  j =  2                              :            45513
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45469
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869469
  j =  1                              :        399909067
  j =  2                              :            45459
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:27.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:19.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:44.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:36.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.07e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.044
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.07
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:47.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.52
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.07
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.94
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.45
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.65
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17165.92
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.78
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.57
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.76
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.97
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.58
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.64
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.37
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.37
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.13
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.67
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.38
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.51
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.45
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.58
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.25
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.46
p-value of test                       :  6.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.76
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.70
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.40
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.53
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.18
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.50
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.32
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.70
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.87
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.99
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.56
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.77
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.36
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.67
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.34
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.09e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.21e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 5.15e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.23
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.30
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.71
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:04.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:06.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9723.60
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10150.19
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:40.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.02
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:47.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.33
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4362.91
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11797.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12131.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:29.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.08
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999930416

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.30
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  7999976322

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9941

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:53.96

 All tests were passed




Server wird beendet - Lösche Semaphor 118554645.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:01.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5307
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:55.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:43.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4439
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:01.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7562
p-value of test                       :  2.3e-3


-----------------------------------------------
CPU time used                    :  00:03:12.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:11.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:05.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:08.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    2.37
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:13.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.25
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:43.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.98
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.31
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.97
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.53
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.96
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.61
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.63
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1335.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7122.81
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.74
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:17.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.10
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.97
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5147.99
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:59.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45873
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869873
  j =  1                              :        399908259
  j =  2                              :            45863
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45812
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869812
  j =  1                              :        399908378
  j =  2                              :            45808
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:32.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:22.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:53.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:08.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.42
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.03
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.23
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.54
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.95
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.52
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.65
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17692.46
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.37
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.57
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.62
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.36
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.50
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.92
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.45
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.38
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.65
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.95
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.80
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.58
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.10
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.61
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.05
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.10
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.50
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.49
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.77
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.19
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.95
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.49
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.61
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.35
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.90
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5124.96
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.28
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.67
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.18
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:23.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.25
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:21.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.83e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 2.39e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.33
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.26
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  2.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.35
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  156.58
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:03.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.7e-3

Kolmogorov-Smirnov- statistic = D-    : 7.91e-4
p-value of test                       :    0.9992    *****

Anderson-Darling statistic = A2       :    5.31
p-value of test                       :  2.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  144.74
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:02:03.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.30
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9852.74
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:04:20.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.15
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:59.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.21
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4265.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11760.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:34.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11953.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:35.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.20
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999931733

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.44
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000065776

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.88
p-value of test                       :    0.03

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 2.83e-3
p-value of test                       :    0.9971

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.87
p-value of test                       :    0.97

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:07.92

 All tests were passed




Server wird beendet - Lösche Semaphor 119570453.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1256
p-value of test                       :    0.9984

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334376
  j =  1                              :        599997488
  j =  2                              :             1256
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5359
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:55.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:05.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7550
p-value of test                       :  3.6e-3


-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:55.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:01.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     953
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    2.24
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    3.86
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:52.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    2.00
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:19.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:46.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.06
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.43
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.01
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.07
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.52
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.74
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.97
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:43.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.87
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7007.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:41.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.92
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.50
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:04.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.93
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.42
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:33.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5110.51
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:16.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45791
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869791
  j =  1                              :        399908424
  j =  2                              :            45779
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45840
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869840
  j =  1                              :        399908322
  j =  2                              :            45836
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:29.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:18.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:59.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 7.94e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:35.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.50
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.26
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.68
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.79
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.57
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.33
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:37.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.46
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17169.95
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.82
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.80
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.79
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.74
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.51
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.79
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.97
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.45
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.60
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.14
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.42
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.03
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.07
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.53
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.45
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.25
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.31
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.82
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.04
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.35
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.21
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.97
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5283.81
p-value of test                       :  2.6e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.52
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.72
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.17
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.42
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5166.40
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.92
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.27
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.40
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -1.58
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.98
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 4.07e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.17e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.11
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.70
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:04.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.24
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:04.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9757.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10172.19
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:38.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.34
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4790.15
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4230.10
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4028.92
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.51
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11838.49
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.88
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999961424

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.01
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000078319

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:07.69

 All tests were passed




Server wird beendet - Lösche Semaphor 120586261.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1501
p-value of test                       :  1.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334621
  j =  1                              :        599996998
  j =  2                              :             1501
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5337
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:54.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:41.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:05.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7165
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:55.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:01.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     831
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9955

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.06
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:16.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.08
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    3.08
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     122
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    1.98
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:45.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.68
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.76
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.88
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.80
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.06
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.15
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.42
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.65
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.15
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7113.73
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.33
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.21
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:00.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.81
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.75
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:32.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5191.85
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:14.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46214
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870214
  j =  1                              :        399907576
  j =  2                              :            46206
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908048
  j =  2                              :            45970
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:27.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:17.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.08e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.20e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:29.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.21
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.75
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.28
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:48.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.57
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.45
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.93
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.08
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17295.16
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.98
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.21
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.01
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.66
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.54
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.87
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.21
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.86
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.90
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.71
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.65
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.02
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.64
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.22
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.37
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.95
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.31
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.12
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.79
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.47
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.27
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.42
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.54
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.24
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.93
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:33.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.09
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.02
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.41
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.94
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.18
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.63
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:11.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.63
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:12.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.17e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 9.94e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.73e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.40
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.47
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.40
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:55.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.86
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:54.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10123.34
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:47.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:19.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.40
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.17
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.32
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.63
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.48
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.81
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000019150

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.04
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000118246

Normal statistic for number of bits   :    0.93
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.16
p-value of test                       :    0.9976

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:57:42.85
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           1.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 121602069.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:49.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5368
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:41.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4460
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:35.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7152
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:33.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:54.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7475
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:00.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7532
p-value of test                       :  6.5e-3


-----------------------------------------------
CPU time used                    :  00:03:00.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:52.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:58.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.96
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:46.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     639
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    2.31
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:13.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     175
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:34.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.75
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.84
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   27.72
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.10
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.45
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.74
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.44
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.29
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7098.77
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.13
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.08
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:03.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.00
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.64
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4933.13
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:58.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45846
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869846
  j =  1                              :        399908313
  j =  2                              :            45836
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46117
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870117
  j =  1                              :        399907768
  j =  2                              :            46113
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:30.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:18.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:59.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:53.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:34.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 9.98e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.95e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 6.65e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.050
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.88
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.85
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.50
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.22
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9932

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.46
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:29.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.28
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17721.21
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.66
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.42
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.00
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.38
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.92
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.98
p-value of test                       :    0.9912


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.03
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.29
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.17
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.44
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.13
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.48
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.54
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.66
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.52
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.36
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.98
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.89
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.78
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.78
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.82
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.16
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.09
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.51
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.49
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.01
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.67
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.39
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.75
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.00
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.78
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:28.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.06
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:21.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 3.86e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.76
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.00
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.07
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:06.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.21
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:08.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.51
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9862.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : -8.01e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:44.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4716.56
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.68
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.68
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4024.12
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11719.32
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11586.78
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.60
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  8000019471

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.08
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999998564

Normal statistic for number of bits   :  -0.011
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         : -7.52e-3
p-value of test                       :    0.50

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:50.22

 All tests were passed




Server wird beendet - Lösche Semaphor 102301718.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:56.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:44.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4461
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:35.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4473
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:54.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:00.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7133
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:01.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:52.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:58.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.65
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:44.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.54
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    2.21
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:09.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    3.98
p-value of test                       :  8.9e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    3.05
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:34.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.15
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.14
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.91
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   83.49
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.36
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  479.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.25
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7007.97
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:44.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.75e-3
p-value of test                       :    0.9941

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.86
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.68
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:03.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.96
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.34
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:32.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.31
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:58.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45872
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869872
  j =  1                              :        399908260
  j =  2                              :            45864
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908203
  j =  2                              :            45891
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:29.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:18.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:02.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 4.83e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:34.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.79
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:48.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.15
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.60
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.73
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.24
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.41
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17500.55
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.51
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.40
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.72
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.55
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.03
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.65
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.09
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   49.26
p-value of test                       :  2.6e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.90
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.99
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.68
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.08
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.25
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.74
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.78
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  433.52
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.08
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.74
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.66
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.96
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5193.05
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.65
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.12
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.45
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.78
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.44
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.41
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.69
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:26.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.21
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    1.80
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:21.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.60e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.69e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.77
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.34
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:09.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.15
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:08.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9936.97
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9731.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:54.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5032.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5038.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.59
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.55
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11733.24
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.43
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000143536

Normal statistic for number of bits   :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.51
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999830801

Normal statistic for number of bits   :   -1.34
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.019
p-value of test                       :    0.49

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:10.59

 All tests were passed




Server wird beendet - Lösche Semaphor 102596614.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:45.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:35.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:54.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:01.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:00.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7500
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:52.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7516
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:57.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    3.51
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     989
p-value of test                       :  1.8e-3

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:10.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:37.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.76
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.62
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.83
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.80
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.18
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  516.05
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:01:44.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7037.37
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:44.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.41
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.09
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:05.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.24
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.72
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:33.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5059.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:55.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45588
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869588
  j =  1                              :        399908828
  j =  2                              :            45580
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45994
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869994
  j =  1                              :        399908014
  j =  2                              :            45990
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:29.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:17.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:44.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:33.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.33e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.96e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:33.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.98
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.45
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.77
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.16
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.2e-3

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.71
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17556.29
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.05
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.83
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.50
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.94
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.07
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.49
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.93
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.31
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.41
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.35
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.99
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.24
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.14
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.76
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.44
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.12
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.43
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.32
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.81
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.30
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.50
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.06
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.68
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.31
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.26
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.00
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.55
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.99
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.86
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.58
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.99
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :  -0.015
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:24.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.67
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:20.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.51e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 8.61e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.40e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.95e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.39
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.31
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.71
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:07.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.70
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:08.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9811.95
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.91
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:58.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.32
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.38
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.92
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.01
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11883.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11811.29
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.35
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000039004

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.71
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999846971

Normal statistic for number of bits   :   -1.21
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         : -2.84e-3
p-value of test                       :    0.50

Sample variance                       :    2.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:26.76

 All tests were passed




Server wird beendet - Lösche Semaphor 103645190.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1480
p-value of test                       :  1.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334600
  j =  1                              :        599997040
  j =  2                              :             1480
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1489
p-value of test                       :  4.5e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334609
  j =  1                              :        599997022
  j =  2                              :             1489
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5474
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:49.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:53.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4176
p-value of test                       :    0.9928


-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:01.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7174
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:02.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:54.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:55.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:11.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.32
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:37.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.28
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.73
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.46
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.38
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.43
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7183.69
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:08.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.67
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.37
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:37.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5143.39
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:01.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45710
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869710
  j =  1                              :        399908587
  j =  2                              :            45696
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46000
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870000
  j =  1                              :        399908003
  j =  2                              :            45994
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:30.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:19.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:02.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.74e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:39.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.94
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.76
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.85
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.17
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.90
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.03
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.85
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.00
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17501.13
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.86
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.88
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.26
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.88
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.37
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.59
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.87
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.21
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.51
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.41
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.55
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.66
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.41
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.67
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.95
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.47
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.08
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.05
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.38
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.72
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.49
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.41
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.09
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.92
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.61
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.31
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.85
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  327.01
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.09
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.15
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:23.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.67
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    1.42
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.15
p-value of test                       :    0.02

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.57e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 5.89e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 6.94e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.91
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.81
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.39
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:03.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.67
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:06.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9884.84
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10115.32
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:04:19.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.62
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:52.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:54.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.69
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.48
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11804.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.56
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:31.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.08
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000139474

Normal statistic for number of bits   :    1.10
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.33
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999948317

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:38.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14           4.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 104660998.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5552
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:48.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:38.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:36.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:02.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:02.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:52.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:56.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.72
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.13
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:02:15.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    2.03
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:47.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.23
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.79
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.91
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.75
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:45.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.49
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6892.91
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   48.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   86.19
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:04.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.47
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.88
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5164.12
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:55.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46324
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870324
  j =  1                              :        399907354
  j =  2                              :            46320
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45508
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869508
  j =  1                              :        399908989
  j =  2                              :            45498
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:28.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :  1.4e-3

Anderson-Darling statistic = A2       :    4.86
p-value of test                       :  3.4e-3


-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:02.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 7.13e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.16e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.21e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:34.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.47
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:47.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.70
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.31
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.71
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.66
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:40.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.62
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.94
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.99
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17427.76
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:52.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.23
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.01
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.85
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.49
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.89
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.71
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.71
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.03
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.10
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.26
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.89
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.32
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.74
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.44
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.60
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.70
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.28
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.99
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.11
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.01
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.89
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.39
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.82
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.38
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.07
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.99
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.55
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.50
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.97
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:24.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.06
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:24.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.70e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.42
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.26
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.61
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.47
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:09.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10152.26
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9974.59
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:47.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.09
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.19
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:51.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.89
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11793.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11838.81
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.58
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999893618

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.17
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999912761

Normal statistic for number of bits   :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:37.13
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP2S, t = 9         0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 105906182.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1488
p-value of test                       :  5.0e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334608
  j =  1                              :        599997024
  j =  2                              :             1488
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:49.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:38.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:36.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:03.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:03.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:53.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     544
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:16.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:46.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.36
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    5.93
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.81
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.59
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.35
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  272.59
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.12
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:45.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1518.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:02.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7242.10
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.61
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 3.70e-3
p-value of test                       :    0.9962

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:03.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.43
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:47.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   87.41
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:34.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5105.90
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:59.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45609
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869609
  j =  1                              :        399908785
  j =  2                              :            45603
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45462
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869462
  j =  1                              :        399909077
  j =  2                              :            45460
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:29.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:18.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.38e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.82e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:35.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:34.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:48.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.94
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.73
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.16
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.72
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:39.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.45
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.44
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17537.01
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.16
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.52
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.41
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.63
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.55
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.86
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.17
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.81
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.97
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.94
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.32
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.98
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  408.32
p-value of test                       :    0.9990


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.30
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.86
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.56
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.58
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.01
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.08
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.78
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.87
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.98
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.46
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.07
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.58
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.41
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.55
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.50
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.66
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.29
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.38
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:22.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.01
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:23.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    0.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.53e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.34e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.49
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.97
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.31
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:07.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:09.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9685.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10185.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.48
p-value of test                       :    0.9934

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:48.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.48
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4730.88
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:50.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4337.62
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.07
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12072.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11548.48
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.62
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000118306

Normal statistic for number of bits   :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.70
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999982763

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:20.80
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14           5.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 106889222.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997303
  j =  2                              :             1347
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5526
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:51.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:38.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:37.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:54.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:04.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:04.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:56.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:56.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    2.77
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.40
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:17.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    3.24
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:47.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.94
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.68
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.16
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.31
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:06.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7084.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.81
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.09
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:08.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.89
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:37.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5099.77
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:53.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45993
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869993
  j =  1                              :        399908021
  j =  2                              :            45979
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45777
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869777
  j =  1                              :        399908447
  j =  2                              :            45775
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:29.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:17.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:45.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:04.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.11e-6
p-value of test                       :    0.9980

Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.58e-4
p-value of test                       :  6.0e-3

Kolmogorov-Smirnov- statistic = D-    : 9.14e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.71
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.63
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.81
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.15
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.82
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.20
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.51
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.34
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
p-value of test                       :    0.9933

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17781.04
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.71
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.68
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.18
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.46
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.56
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.24
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.81
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.51
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.21
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.87
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.95
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.77
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.60
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.29
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.55
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.14
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.02
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.59
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.93
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.75
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.39
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.25
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.27
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.67
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.13
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4780.81
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.73
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.62
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.92
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:24.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.40
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -1.49
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:23.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9986

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.23e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.63
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.96
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.15
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:06.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.18
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:05.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9813.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.77
p-value of test                       :  3.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9614.18
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:04:17.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.68
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:52.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:54.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.11
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11915.36
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:31.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11438.83
p-value of test                       :    0.9944

-----------------------------------------------
CPU time used                    :  00:01:30.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.01
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000031900

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.72
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999963986

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    2.77
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:44.61

 All tests were passed




Server wird beendet - Lösche Semaphor 107872262.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5506
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:51.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:38.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:05.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:55.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:00.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    2.38
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:15.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:43.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.96
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.44
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.68
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.03
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.75
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.16
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.49
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.17
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1381.84
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:06.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7169.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.78e-3
p-value of test                       :    0.9941

Kolmogorov-Smirnov- statistic = D-    :    0.60
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.35
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:09.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.42
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.17
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:37.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5075.49
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:16.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45768
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869768
  j =  1                              :        399908469
  j =  2                              :            45758
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45598
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869598
  j =  1                              :        399908808
  j =  2                              :            45590
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:30.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:18.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
p-value of test                       :    0.9923

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-6
p-value of test                       :    0.9999    *****

Kolmogorov-Smirnov- statistic = D-    : 3.35e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.22
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.62
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.89
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.81
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.10
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   49.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.42
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.81
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17340.54
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.30
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.93
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.69
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.98
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.58
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.41
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.37
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.86
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.67
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.66
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.71
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.16
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.81
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.66
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.70
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.87
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.41
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.81
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.02
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.41
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.42
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4726.88
p-value of test                       :    0.9972


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.40
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.78
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.24
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.17
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.15
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.70
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.90
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.54
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.91
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.0e-3

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.88
p-value of test                       :    0.03

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 3.70e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 9.66e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.01
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.11
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.98
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.29
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.58
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9782.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:04:19.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4799.18
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:53.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:53.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.54
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11714.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.13
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999948725

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.91
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000126607

Normal statistic for number of bits   :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:36.28

 All tests were passed




Server wird beendet - Lösche Semaphor 108920838.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5280
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:51.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:39.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4464
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7155
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:03.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:54.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:59.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     646
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:16.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:44.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.89
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    4.92
p-value of test                       :    0.9990

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.55
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.37
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.70
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.93
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.78
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:02.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7010.76
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.73
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:03.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.99
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.25
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5002.41
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:10.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45928
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869928
  j =  1                              :        399908147
  j =  2                              :            45922
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45680
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869680
  j =  1                              :        399908644
  j =  2                              :            45672
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:17.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:01.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:54.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:33.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.10e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 3.80e-4
p-value of test                       :  3.1e-3

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.36
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.96
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.09
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.82
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.17
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.96
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17400.48
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.01
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.75
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.16
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.20
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.31
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.92
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.78
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.46
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.19
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  101.57
p-value of test                       :    0.9980


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.71
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.85
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.19
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.57
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.85
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.89
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.44
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.64
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.40
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.89
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.83
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.38
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.73
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.73
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.41
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.51
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.58
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.31
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.11
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.08
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.72
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:22.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.40e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.04
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.73
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.22
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:04.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.99
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10179.98
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10052.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:42.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.17
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3984.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3962.22
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11824.13
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11770.93
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.58
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999903392

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.13
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999920993

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 5.84e-3
p-value of test                       :    0.9938

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.75
p-value of test                       :    0.96

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.93

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:17.03

 All tests were passed




Server wird beendet - Lösche Semaphor 110100486.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5409
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:52.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:39.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4497
p-value of test                       :  7.9e-3


-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:03.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:02.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:53.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:59.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.42
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:16.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:45.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.30
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.47
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.48
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.29
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1484.41
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:04.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7013.75
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
p-value of test                       :    0.9944

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:11.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   16.74
p-value of test                       :  5.0e-3


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.94
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:35.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5240.16
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:14.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46013
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870013
  j =  1                              :        399907979
  j =  2                              :            46003
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45987
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869987
  j =  1                              :        399908030
  j =  2                              :            45979
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:29.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:17.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:59.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  9.9e-3

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:32.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.33
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.53
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.03
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.75
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.42
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:43.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.57
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.72
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17484.13
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.90
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.53
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.00
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.29
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.01
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.99
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.12
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.60
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.36
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.31
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.33
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  103.98
p-value of test                       :    0.9966


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.65
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.71
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.82
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.47
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.36
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.21
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5168.51
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.15
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.18
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.27
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.56
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.38
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  436.78
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.82
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.90
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:23.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.84
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:24.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 7.62e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.50e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.13e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.77
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.78
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:07.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.64
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9967.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.27
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:04:07.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.03
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4974.30
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.63
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.74
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11912.87
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:30.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.21
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000097192

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.78
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000054373

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.60
p-value of test                       :    0.95

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    2.92
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:48.45

 All tests were passed




Server wird beendet - Lösche Semaphor 111083526.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997193
  j =  2                              :             1402
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5513
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:54.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:03.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:03.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:54.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:59.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.92
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    2.48
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     340
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:12.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.40
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:39.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.18
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.32
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.63
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.86
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:45.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7179.57
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.33
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.7e-3

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.52
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:04.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.32
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.64
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5024.08
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:01.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46036
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870036
  j =  1                              :        399907937
  j =  2                              :            46018
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45743
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869743
  j =  1                              :        399908518
  j =  2                              :            45735
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:27.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  9.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.70
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:18.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:45.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 8.61e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:02.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 7.91e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.062
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:35.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.90
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.42
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.12
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:47.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.73
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.31
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.97
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.59
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.78
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   93.08
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17146.22
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.16
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.95
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.89
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.54
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.63
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.64
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.50
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.39
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.01
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.84
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.19
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.86
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.65
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.54
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.76
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.80
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.41
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.43
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.58
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.77
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.59
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.22
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.86
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.56
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.16
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.17
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.32
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.35
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  429.80
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.11
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.86
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   0.092
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:25.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.93
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -1.26
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:23.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 4.86e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.33e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.89
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.27
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:04.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:06.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10138.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.55
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:42.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4794.98
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:50.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.66
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11685.72
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12206.42
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.62
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000129421

Normal statistic for number of bits   :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.97
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999956384

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9924

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:42.15

 All tests were passed




Server wird beendet - Lösche Semaphor 112066566.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:58.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:44.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:00.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4185
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:01.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:10.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:10.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:08.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:13.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.86
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:11.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.80
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    2.36
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:44.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.08
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.81
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.38
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.03
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.56
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.81
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.03
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:58.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.42
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:10.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7244.07
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:56.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:09.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.22
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.82
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:40.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4965.78
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:01.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45753
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869753
  j =  1                              :        399908498
  j =  2                              :            45745
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45845
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869845
  j =  1                              :        399908312
  j =  2                              :            45841
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:29.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:12.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:57.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:39.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.54e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.36e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:24.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.096
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:54.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.10
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.07
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.81
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.31
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.37
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:51.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.97
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.39
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.89
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17559.49
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.25
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.20
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.29
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.90
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.22
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.26
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.79
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.03
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.51
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.06
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.71
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.80
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.52
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.67
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.94
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.55
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.27
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.35
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.52
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.98
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.40
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.91
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.70
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.42
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.83
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.72
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.94
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.81
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.02
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.80
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:23.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.41
p-value of test                       :    0.9920

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.08e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.79
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.43
p-value of test                       :    0.9938

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:38.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.50
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:28.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.20
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10290.64
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.83
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:04:39.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:52.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4801.47
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:55.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.46
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.85
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11962.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11936.79
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:35.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.67
p-value of test                       :  8.9e-3


-----------------------------------------------
Total number of bits:  8000001852

Normal statistic for number of bits   :   0.015
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.67
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000042811

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :  -0.024
p-value of test                       :    0.51

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:04.39

 All tests were passed




Server wird beendet - Lösche Semaphor 112984070.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1252
p-value of test                       :    0.9989

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334372
  j =  1                              :        599997496
  j =  2                              :             1252
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5494
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:57.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:59.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:10.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7092
p-value of test                       :    0.9960


-----------------------------------------------
CPU time used                    :  00:04:08.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:14.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:51.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:19.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    2.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:45.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.83
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.68
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.32
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.89
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.17
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.85
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:59.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.24
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:09.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7106.04
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:59.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   88.89
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.83
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.49
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5272.12
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:03.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45989
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869989
  j =  1                              :        399908025
  j =  2                              :            45983
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45545
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869545
  j =  1                              :        399908911
  j =  2                              :            45543
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:31.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:20.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:54.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:10.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:56.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:24.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:53.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.29
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.17
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.15
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.65
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.29
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.12
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.26
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.07e-3
p-value of test                       :    0.9958

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17035.20
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.61
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.73
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.97
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.12
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.52
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.48
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.48
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.81
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.90
p-value of test                       :    0.9939


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.51
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.26
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.50
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.42
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.93
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.09
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.07
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.36
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.52
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.62
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.72
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.68
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5122.99
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.41
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.11
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.37
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.10
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.43
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.35
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.78
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.53
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:21.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.74
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    1.80
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:22.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.83

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.23e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 8.49e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.76e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 7.16e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.73
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.60
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.2e-3

Anderson-Darling statistic = A2       :    3.68
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:05.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.6e-3

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:05.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.55
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9720.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:11.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.23
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:04:34.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.58
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:57.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 8.95e-3
p-value of test                       :    0.9903

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4696.47
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.52
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.19
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11948.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:36.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11990.21
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.41
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999962363

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.80
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000051934

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :  -0.090
p-value of test                       :    0.54

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:22.13

 All tests were passed




Server wird beendet - Lösche Semaphor 114360326.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5384
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:52.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4231
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:07.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:11.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     650
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    2.11
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    2.61
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:19.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.81
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:48.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.09
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.59
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.76
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.25
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.25
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.52
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:29.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.21
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1455.90
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:08.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6996.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   36.22
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:03:17.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.16
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.32
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:40.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5156.93
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:01.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45993
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869993
  j =  1                              :        399908020
  j =  2                              :            45981
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45876
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869876
  j =  1                              :        399908251
  j =  2                              :            45870
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:31.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:21.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:51.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:24.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.03
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.41
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.07
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.63
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.21
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.95
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:52.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.65
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.24
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.14
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.09
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17230.44
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:52.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.03
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.29
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.65
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.48
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.53
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.26
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.35
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.20
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.56
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.31
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.29
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.97
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.00
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.95
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.45
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.83
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  103.98
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.87
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.16
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.51
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.05
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.15
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.61
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.05
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.62
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.86
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.57
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.91
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:23.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.73
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:21.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.18
p-value of test                       :    0.01

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.86e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.85e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.59
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.15
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.99
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:05.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.20
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:05.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10205.85
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9917.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:04:22.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.45
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:55.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4793.67
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:58.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4006.39
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4270.35
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.74
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:35.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11686.56
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:35.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.41
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999987896

Normal statistic for number of bits   :  -0.096
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.80
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999939770

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.018
p-value of test                       :    0.49

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:55.96

 All tests were passed




Server wird beendet - Lösche Semaphor 115605510.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:48.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.33

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5411
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:55.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:05.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:05.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:56.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:02.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:50.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     260
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:20.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:47.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.01
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.61
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.99
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.16
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.09
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.32
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  477.62
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:01.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6893.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.93
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:02.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.06
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.32
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:33.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5030.79
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:56.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46143
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870143
  j =  1                              :        399907717
  j =  2                              :            46137
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45743
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869743
  j =  1                              :        399908519
  j =  2                              :            45733
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:28.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:19.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9978


-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:01:32.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.81e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:38.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.62
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.89
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.19
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.29
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17530.95
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.00
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.05
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.37
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.00
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.09
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.75
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.92
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.95
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.22
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.85
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.94
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.46
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.71
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.27
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.56
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.52
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.96
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.95
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.32
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.33
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.24
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4826.82
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.89
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  158.81
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.60
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.79
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.94
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.96
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.38
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.69
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.54
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.53e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 7.37e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.80e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 9.75e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.04
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.26
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.10
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:02.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.81
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:03.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10116.77
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.60
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:37.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.68e-3
p-value of test                       :    0.9940

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5094.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:50.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.76
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4223.67
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11461.15
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.64
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999982550

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.45
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000054754

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:42.65

 All tests were passed




Server wird beendet - Lösche Semaphor 116654086.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:48.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5386
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:56.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:05.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:05.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:57.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:04:01.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:18.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.13
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9935

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:47.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.58
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.94
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.91
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.04
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.67
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.81
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.55
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.55
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.08
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:01.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7064.29
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:41.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.34
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.61
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:03.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.83
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.10
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:33.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5132.03
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:58.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46228
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870228
  j =  1                              :        399907553
  j =  2                              :            46210
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45566
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869566
  j =  1                              :        399908870
  j =  2                              :            45562
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:28.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:18.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:44.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:54.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 8.77e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:40.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:38.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.28
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.01
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.62
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.46
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.30
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.76
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.11
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.47
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.78
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17867.82
p-value of test                       :  9.9e-3



-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.04
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.88
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.66
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.84
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.47
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.13
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.35
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.41
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.99
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.41
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.89
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.61
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.95
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.93
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.04
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.25
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.28
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.27
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.63
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.69
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.18
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.17
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.89
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.22
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.88
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.58
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.16
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.91
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.17
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.40
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :  -0.073
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:21.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.11
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 7.67e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.01e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.78
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.97
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.11
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.64
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:05.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.01
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:40.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5061.40
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.60
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:50.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.18
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11642.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11853.66
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.77
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999965711

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.82
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999958628

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.44
p-value of test                       :    0.07

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:49.01

 All tests were passed




Server wird beendet - Lösche Semaphor 117604358.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:48.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:56.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:43.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:58.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:59.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:08.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:08.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:00.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:03.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    2.22
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:50.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:18.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:49.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.11
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.96
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.84
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.83
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.33
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1499.61
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:01.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7271.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.12
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.13
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:09.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.64
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.24
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:37.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5010.94
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:59.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45854
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869854
  j =  1                              :        399908294
  j =  2                              :            45850
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45519
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869519
  j =  1                              :        399908963
  j =  2                              :            45517
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:31.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.18e-3
p-value of test                       :    0.9977

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:02.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.36
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.91
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.59
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.76
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.80
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.25
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.94
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.09
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17591.97
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.67
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.95
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.82
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.57
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.29
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.42
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.87
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.35
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.03
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.67
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.27
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.17
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.12
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.36
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.69
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.79
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.35
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.78
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.91
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.46
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.04
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.78
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.53
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.85
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.18
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.10
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.35
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.48
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:21.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.17e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.35e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.97
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.99
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.40
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:05.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10163.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:04:12.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4999.41
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:52.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.80
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:53.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4208.16
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.32
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11760.38
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12027.56
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.78
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999959990

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.67
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999973616

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         : 6.92e-3
p-value of test                       :    0.50

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.92

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:14.17

 All tests were passed




Server wird beendet - Lösche Semaphor 118620166.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5515
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:55.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:05.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:05.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:54.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:00.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    3.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:13.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:46.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.52
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.30
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.08
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.75
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.78
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.90
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.49
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.12
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.22
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:43.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.88
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7107.00
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.86
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.71
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:04.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.97
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.13
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4816.95
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:54.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45698
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869698
  j =  1                              :        399908607
  j =  2                              :            45692
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45780
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869780
  j =  1                              :        399908446
  j =  2                              :            45768
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:29.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:19.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:00.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.03e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 3.12e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:33.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.23
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.58
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.73
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.77
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.52
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.68
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.99
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.07
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17395.78
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.75
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.73
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.00
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.61
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.55
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.18
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.61
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.61
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.55
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.41
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.09
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.34
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.23
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.35
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  107.52
p-value of test                       :  6.6e-3


-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.29
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.66
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.34
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.83
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.12
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.95
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.46
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4837.71
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.19
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.66
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.02
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.97
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.29
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.66
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.56
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:20.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.40
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:22.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.07e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.77e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 4.76e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.73
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.43
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.07
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:04.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.34
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:05.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.26
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9868.03
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:38.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.74
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:48.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.01
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11608.88
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11601.52
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:29.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.45
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000054172

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.68
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999975506

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.058
p-value of test                       :    0.52

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    2.71
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :  -0.042
p-value of test                       :    0.52

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:41.79

 All tests were passed




Server wird beendet - Lösche Semaphor 119635974.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1492
p-value of test                       :  3.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334612
  j =  1                              :        599997016
  j =  2                              :             1492
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5574
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:57.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4193
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:08.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:07.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:59.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:03.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.38
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.39
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:42.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.95
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.64
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.03
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.45
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.59
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1382.11
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:04.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6943.40
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:51.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.48
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.33
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:11.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.64
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.04
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5124.34
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9901


-----------------------------------------------
CPU time used                    :  00:02:59.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45845
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869845
  j =  1                              :        399908314
  j =  2                              :            45837
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45767
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869767
  j =  1                              :        399908474
  j =  2                              :            45751
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  8.3e-3

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:31.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:20.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:07.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:39.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.72e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.051
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.058
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.50
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.25
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.02
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:08.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.80
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.32
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17543.53
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.98
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.86
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.19
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.41
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.12
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.84
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.45
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.16
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.10
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.22
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.35
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.46
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.14
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.75
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.93
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.86
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.86
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.32
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.92
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.82
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5100.24
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.98
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.32
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.91
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.46
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.34
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.10
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.22
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.45
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:21.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.74
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -1.37
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:20.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 6.37e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.55e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.13
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.80
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.21
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:03.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.61
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:04.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10186.56
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9889.69
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.024
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:04:16.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.24
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:53.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4765.97
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.77
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4238.14
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11799.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11642.21
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:32.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.80
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000076336

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.19
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000037897

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:02.18
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           3.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 120619014.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5358
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:55.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:04.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:04.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7471
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:01.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    2.62
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    5.94
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.76
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    3.28
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:15.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:45.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.89
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.79
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.78
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.69
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.39
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.57
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7211.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:43.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.45
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.73
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:04.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.33
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.81
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:35.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5034.85
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:56.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45729
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869729
  j =  1                              :        399908548
  j =  2                              :            45717
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45947
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869947
  j =  1                              :        399908108
  j =  2                              :            45943
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:28.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:18.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:44.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:54.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.82e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 2.55e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.56e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.63
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.63
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.78
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.83
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.77
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.53
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17285.13
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:48.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.04
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.78
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.65
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.01
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.16
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:34.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.40
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.48
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.02
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.84
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.72
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:34.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.52
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.13
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.02
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.97
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.01
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.07
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.97
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.28
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.52
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.26
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5112.76
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.26
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.16
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.96
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.52
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.43
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.49
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.29
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.09
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:11.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.58
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -1.19
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:11.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.75e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.52e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:40.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.89
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.03
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:53.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.27
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:54.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9770.44
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:19.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.47
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:37.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.13
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.58
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.25
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.95
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.66
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999970637

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.31
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999983702

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.060
p-value of test                       :    0.48

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:56:48.70

 All tests were passed




Server wird beendet - Lösche Semaphor 121700358.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:42.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:34.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4210
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:53.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:01.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:01.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7508
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:59.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    3.76
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     972
p-value of test                       :  9.2e-3

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.86
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:08.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:38.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.47
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.34
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.41
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.09
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.31
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  179.22
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.77
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7005.57
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.5e-3

Anderson-Darling statistic = A2       :    4.81
p-value of test                       :  3.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   95.02
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:03:08.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.00
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:38.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5178.86
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:18.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45714
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869714
  j =  1                              :        399908576
  j =  2                              :            45706
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45694
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869694
  j =  1                              :        399908619
  j =  2                              :            45680
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  8.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:29.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  8.2e-3

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:16.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:43.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:57.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:53.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:35.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.36e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 3.35e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.55
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.035
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.25
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.08
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.26
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.50
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.98
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17201.40
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.34
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.93
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.71
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.89
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.09
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.24
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.46
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.47
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.13
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.49
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.27
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.80
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.66
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.24
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.06
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.89
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.58
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.03
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.78
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.01
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.01
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.91
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.81
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.04
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.03
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.43
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.36
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.66
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.60
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.07
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :    1.16
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:25.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.29
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :   -1.50
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:25.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.34e-3
p-value of test                       :    0.9922

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    4.94
p-value of test                       :  3.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.12
p-value of test                       :  8.9e-4    *****

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.37e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 8.63e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.47e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.28
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.72
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.10
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:07.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.56
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:10.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10156.51
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:04:18.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4769.18
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:52.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4759.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:53.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.35
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.85
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12001.81
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:32.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11734.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.39
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000100075

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.36
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999894599

Normal statistic for number of bits   :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.38
p-value of test                       :  8.5e-3

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9913

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:16:21.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 82  LempelZiv, r = 0                8.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 102334487.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:46.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4496
p-value of test                       :  8.2e-3


-----------------------------------------------
CPU time used                    :  00:01:37.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:36.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:53.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:03.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:03.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7145
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:54.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:58.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.59
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:13.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    3.02
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.74
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.57
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.99
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.55
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.11
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.90
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.37
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1362.70
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:06.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7121.77
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.36
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   87.11
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.40
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.45
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:37.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4988.43
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:00.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45502
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869502
  j =  1                              :        399909001
  j =  2                              :            45492
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45862
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869862
  j =  1                              :        399908278
  j =  2                              :            45858
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  5.1e-3

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:28.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:16.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:42.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:01.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.093
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.51
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.30
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.40
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.33
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.49
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.79
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:46.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.21
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.64
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.02
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.28
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17584.70
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.58
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.89
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.12
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.37
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.94
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.67
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   44.75
p-value of test                       :  8.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.20
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.73
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.12
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.82
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.46
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.63
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.99
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.91
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.98
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.83
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.50
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.47
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.67
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.72
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.77
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.41
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  154.48
p-value of test                       :    0.9927


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.90
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.55
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4893.96
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  318.64
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.74
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.70
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:21.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.74
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.2e-3

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 3.64e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.92
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.63
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:10.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.48
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10004.89
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10178.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.032
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:04:18.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:52.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4933.30
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:56.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4290.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.64
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:30.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.47
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000053296

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.70
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000067504

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   0.046
p-value of test                       :    0.48

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :  -0.059
p-value of test                       :    0.52

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:53.56

 All tests were passed




Server wird beendet - Lösche Semaphor 103186455.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5447
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:49.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4223
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:38.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7167
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:06.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:06.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:04.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:09.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.26
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    2.40
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:15.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:40.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.01
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.22
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.91
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.20
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.25
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  275.40
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.60
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:59.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1374.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:08.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7129.07
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:04.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:02.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.08
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.42
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:33.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4800.38
p-value of test                       :    0.9920


-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:57.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908167
  j =  2                              :            45909
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45437
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869437
  j =  1                              :        399909129
  j =  2                              :            45431
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:26.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:19.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:51.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:08.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 3.49e-3
p-value of test                       :    0.9963

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.54e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 3.27e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-5
p-value of test                       :    0.9940

Kolmogorov-Smirnov- statistic = D-    : 3.02e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.96
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.45
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.21
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.71
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.68
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:53.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.17
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.51
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17323.27
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.71
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   67.94
p-value of test                       :  7.0e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.32
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.94
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.96
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.71
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.91
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.16
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.45
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.23
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.92
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.17
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.69
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.80
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.88
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.16
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.60
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.19
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.63
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.97
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  305.31
p-value of test                       :    0.9988


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.88
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5141.54
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.03
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.65
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.31
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.17
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.60
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.56
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.54
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :    1.30
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:23.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.39
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:26.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.087
p-value of test                       :    0.47

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:47.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 2.73e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.26
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:31.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.08
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:16.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.28
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:17.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10171.08
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10060.35
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:51.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.51
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:52.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.05
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:53.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.33
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.30
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12031.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11895.91
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.63
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000108634

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.39
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999925859

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.89
p-value of test                       :    0.97

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.16
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:37.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 M (L=50, r=0)       7.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 104398871.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1480
p-value of test                       :  1.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334600
  j =  1                              :        599997040
  j =  2                              :             1480
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5370
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:50.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:40.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:06.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:06.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7498
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:06.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:14.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9926

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:14.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:41.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.13
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.48
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.71
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.52
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.12
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.44
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7190.53
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:03.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.78
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.66
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:16.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.13
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.93
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5095.20
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:54.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45938
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869938
  j =  1                              :        399908129
  j =  2                              :            45928
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46260
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870260
  j =  1                              :        399907486
  j =  2                              :            46248
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:30.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:22.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:53.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :  2.4e-3

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:08.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:57.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.49e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 6.52e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.57
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.97
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.51
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.48
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.85
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.36
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:53.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.18
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 3.01e-4
p-value of test                       :    0.9997    *****

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.84
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17326.96
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.61
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.65
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.50
p-value of test                       :    0.9963


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.95
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.16
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.65
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.20
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.11
p-value of test                       :    0.9924


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.77
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.98
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  563.62
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.59
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.22
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.53
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.26
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  572.01
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.64
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.18
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.86
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.22
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5141.76
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.30
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.46
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.90
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.88
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4778.84
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.68
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.87
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.55
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.61
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:25.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -2.05
p-value of test                       :    0.98

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.61e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.81e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 6.82e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.39
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:41.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.34
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:39.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:30.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.43
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:30.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10043.62
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.059
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:04:38.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5072.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:54.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4996.14
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4008.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11838.34
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11834.98
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:32.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.44
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999919076

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.92
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999921158

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         : -9.98e-3
p-value of test                       :    0.50

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.44e-3
p-value of test                       :    0.9954

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.7e-3

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.42
p-value of test                       :  7.8e-3

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:39.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:41.89

 All tests were passed




Server wird beendet - Lösche Semaphor 105316375.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:55.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:41.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:40.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:03.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:54.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:01.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.19
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:13.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:43.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.13
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.13
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.72
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  280.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  538.82
p-value of test                       :  4.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.65
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:03.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7090.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:43.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.00
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:06.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.82
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.01
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5208.86
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:11.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:56.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46318
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870318
  j =  1                              :        399907369
  j =  2                              :            46308
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45757
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869757
  j =  1                              :        399908489
  j =  2                              :            45751
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:28.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:18.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:58.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:35.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.32e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:43.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.06
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.45
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.47
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.81
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.60
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.83
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.93
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.56
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.89
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17552.19
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.40
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.52
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.43
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.80
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.69
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.55
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   53.77
p-value of test                       :  7.1e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   43.12
p-value of test                       :  9.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.08
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.19
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.55
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.69
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.53
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.91
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.40
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.87
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.56
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.17
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.15
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  306.87
p-value of test                       :    0.9985


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.22
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5136.08
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.33
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  265.49
p-value of test                       :  1.3e-3


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.68
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.10
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.07
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.56
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.87
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.15
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:23.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.58
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.55e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 6.34e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.43e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.07
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.55
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:04.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.68
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9840.17
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10227.19
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:38.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.19
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:45.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.90
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3980.80
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.07
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11777.70
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11653.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.60
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000017779

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.46
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000034090

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:55.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 35  Gap, r = 25                     4.4e-4
 75  RandomWalk1 J (L=50, r=25)      7.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 106594327.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:48.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:54.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:05.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:05.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:56.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:02.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:46.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    2.28
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:14.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:45.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.99
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.78
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.17
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.12
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.34
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.29
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1386.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6987.19
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:41.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.43
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:06.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.45
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.16
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5105.09
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:52.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45757
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869757
  j =  1                              :        399908489
  j =  2                              :            45751
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46077
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870077
  j =  1                              :        399907852
  j =  2                              :            46065
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:26.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:17.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 5.75e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.12e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.21
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.96
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.78
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.12
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.55
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.24
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.62
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17546.58
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.90
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.40
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.76
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.36
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.89
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.63
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.88
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.83
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.55
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.03
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.04
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.03
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.32
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.15
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.15
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.59
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.84
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.90
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.43
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.25
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5191.28
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.55
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.63
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.43
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.01
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5164.39
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.30
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.84
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.97
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :   0.030
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:23.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.54
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.83e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 5.23e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 7.82e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.94
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.27
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.54
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:04.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.19
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10059.66
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10048.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:48.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5001.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:46.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4734.44
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4280.01
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.95
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12093.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12032.07
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.86
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999980627

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.96
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000009907

Normal statistic for number of bits   :   0.078
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.66

Sample variance                       :    0.20
p-value of test                       :    0.9943

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:33.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:29.84

 All tests were passed




Server wird beendet - Lösche Semaphor 107577367.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:49.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1255
p-value of test                       :    0.9986

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334375
  j =  1                              :        599997490
  j =  2                              :             1255
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1487
p-value of test                       :  5.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334607
  j =  1                              :        599997026
  j =  2                              :             1487
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5532
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:56.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:43.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:59.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4448
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:01.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7493
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:11.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:11.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7157
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:16.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.52
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.67
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    2.34
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:15.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:44.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.83
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.93
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.68
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.58
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.81
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:56.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.74
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6847.48
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:59.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.03
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.27
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:20.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.32
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:46.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.70
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4927.66
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:56.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45975
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869975
  j =  1                              :        399908052
  j =  2                              :            45971
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46162
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870162
  j =  1                              :        399907678
  j =  2                              :            46158
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:31.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:21.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:52.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:08.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:38.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.38e-5
p-value of test                       :    0.9924

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 4.47e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : 7.22e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.060
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:51.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.65
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.32
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.23
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.31
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.68e-3
p-value of test                       :    0.9983

Anderson-Darling statistic = A2       :    3.50
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   95.32
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17556.11
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.83
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.37
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.55
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.21
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.29
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.60
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.77
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.05
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.02
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.86
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.58
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.63
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.15
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.14
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.68
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.49
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.83
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.42
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.58
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.16
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.05
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.70
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.27
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.60
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.63
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.33
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.03
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.92
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.90
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.39
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.99
p-value of test                       :  7.7e-3


-----------------------------------------------
Normal statistic for number of jumps  :   -1.64
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.40
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:22.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.94e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.16
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.83
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.66
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:04.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.77
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:04.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10071.77
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9899.73
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:04:23.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.83
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:57.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9938

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.01
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:01.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4230.29
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11847.30
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:36.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11399.34
p-value of test                       :    0.9974

-----------------------------------------------
CPU time used                    :  00:01:37.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.11
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000079954

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.04
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000107701

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :  -0.024
p-value of test                       :    0.51

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:53.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           5.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 108593175.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:54.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:57.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:06.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:07.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:59.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:01.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    2.91
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:17.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    2.89
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:43.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.06
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.14
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.33
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.06
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.20
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.27
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1378.70
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:02.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7099.43
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.53
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 2.24e-3
p-value of test                       :    0.9977

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.98
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:05.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.38
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.59
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.30
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:53.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45883
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869883
  j =  1                              :        399908236
  j =  2                              :            45879
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45623
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869623
  j =  1                              :        399908757
  j =  2                              :            45617
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:28.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:16.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:57.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:36.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.66e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.86e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.42
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.45
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  111.88
p-value of test                       :  4.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.64
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.19
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.30
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.97
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   12.59
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.15
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.11
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.51
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.21e-3
p-value of test                       :    0.9923

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16975.08
p-value of test                       :    0.9929



-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.69
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.86
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.00
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.64
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.13
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.49
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.79
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.46
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.76
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.58
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.63
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.83
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.39
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.32
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.63
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.16
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.32
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.75
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.98
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.25
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.34
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5234.21
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.90
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.28
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.25
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.59
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.37
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.94
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.90
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.56
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.62
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:23.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 7.68e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.67e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.84
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.48
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:04.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.66
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:03.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10176.45
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10184.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:35.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.42
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.76
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11981.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11839.71
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.87
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999972128

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.77
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999809621

Normal statistic for number of bits   :   -1.51
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.82
p-value of test                       :    0.03

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   0.061
p-value of test                       :    0.48

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:17.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 60  WeightDistrib, r = 20           4.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 109674519.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1267
p-value of test                       :    0.9959

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334387
  j =  1                              :        599997466
  j =  2                              :             1267
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:52.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4463
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:05.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:05.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:55.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:00.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.16
p-value of test                       :    0.9979


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:17.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:46.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.32
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.69
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.07
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.30
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.22
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.92
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.05
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.82
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:44.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7218.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.91
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:02.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.03
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.77
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:33.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5126.22
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:58.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45984
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869984
  j =  1                              :        399908035
  j =  2                              :            45978
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45913
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869913
  j =  1                              :        399908179
  j =  2                              :            45903
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:28.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:01.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:57.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 7.51e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.26e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:39.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.69
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.61
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.85
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.97
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.46
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:38.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.42
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.27
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17294.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.61
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.14
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.83
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.83
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.29
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.87
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.46
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.05
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.63
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.01
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.41
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  426.62
p-value of test                       :    0.9923


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.16
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.68
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.00
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.88
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.69
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.05
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.59
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.32
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.60
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.79
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.64
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.20
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.97
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.29
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.73
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.27
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.77
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.83
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:24.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.47
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:24.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.15e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 7.72e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.76
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.17
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.88
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:06.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9871.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10265.38
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:32.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.70
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4006.86
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4221.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11921.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.49
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.03
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000039607

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.92
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999976493

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    2.35
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.66e-3
p-value of test                       :    0.9951

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:41.29

 All tests were passed




Server wird beendet - Lösche Semaphor 110657559.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:40.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1477
p-value of test                       :  1.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334597
  j =  1                              :        599997046
  j =  2                              :             1477
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:55.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:44.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:02.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:13.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:11.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7122
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:04:15.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.93
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     552
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    2.83
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.89
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:18.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:48.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.18
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.66
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.00
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.98
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.59
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.87
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:59.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:09.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7097.95
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.92
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:16.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.68
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.19
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:42.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5136.33
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:05.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45693
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869693
  j =  1                              :        399908616
  j =  2                              :            45689
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46172
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870172
  j =  1                              :        399907662
  j =  2                              :            46160
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:32.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:21.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:52.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:08.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:37.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 6.46e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.59e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:54.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.77
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.37
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.97
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.02
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.50
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.18
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.55
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17390.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.03
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.96
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.19
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.84
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.14
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.56
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.59
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.08
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.51
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.34
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.92
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.96
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.66
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.59
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.11
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.34
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.02
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.93
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.90
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.51
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.41
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.45
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.70
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.82
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.60
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4841.60
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.23
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.10
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.17
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:21.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.91
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:21.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 2.86e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.12e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.28
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.60
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.37
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:03.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.65
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:03.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.53
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:04:23.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5002.40
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:56.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.04
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:00.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3975.47
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.68
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:29.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11992.05
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.94
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.55
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000061765

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.92
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999970646

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:44.87

 All tests were passed




Server wird beendet - Lösche Semaphor 111640599.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5352
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:55.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:43.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:01.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:12.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:09.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:07.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.21
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:15.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:42.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.71
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.01
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.12
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  282.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  477.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:51.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.82
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:05.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6960.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:54.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.96
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:13.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.65
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.13
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:37.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4958.87
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:01.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45831
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869831
  j =  1                              :        399908342
  j =  2                              :            45823
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45939
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869939
  j =  1                              :        399908129
  j =  2                              :            45925
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:32.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:20.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:52.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:07.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
p-value of test                       :    0.9902

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 9.51e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.21
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.15
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.64
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.04
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.91
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  100.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17467.33
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   60.35
p-value of test                       :  6.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.65
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.21
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.52
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.88
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.67
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.68
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.76
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.36
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.55
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.86
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.52
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.63
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.50
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.13
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.90
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.56
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.64
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.09
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.17
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5117.00
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.37
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.42
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.64
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.61
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5137.34
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.95
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.51
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.03
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -0.79
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:20.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.62
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:21.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 2.40e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.22
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.88
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:03.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.63
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:02.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10117.05
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-3
p-value of test                       :    0.9986

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10365.29
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:04:10.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.62
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:54.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4208.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.65
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11955.98
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:31.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12036.07
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:32.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.36
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000106801

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.28
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999978692

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:10.37

 All tests were passed




Server wird beendet - Lösche Semaphor 112721943.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5353
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:56.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:41.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:57.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:06.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:07.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:56.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:00.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.17
p-value of test                       :    0.9964

Test on the Nm values of W_{n,i}(mNP1):    1.95
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.65
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:12.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:43.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.30
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.30
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   23.80
p-value of test                       :    0.9999    *****

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.88
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.57
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.69
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:43.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:59.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7055.32
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.35
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:02.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.77
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.56
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5107.15
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:58.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45785
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869785
  j =  1                              :        399908433
  j =  2                              :            45779
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45860
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869860
  j =  1                              :        399908281
  j =  2                              :            45858
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:29.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:58.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:55.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.73e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 2.57e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.030
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:38.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    3.30
p-value of test                       :  4.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:37.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.66
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.00
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.30
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:40.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.33
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.88
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.84
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17379.42
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.66
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.67
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.66
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.28
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.20
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.40
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.89
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.68
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.01
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.17
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.95
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.40
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.59
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.82
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.19
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   43.61
p-value of test                       :    0.9981


-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.82
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.58
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4899.55
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.61
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4799.55
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.65
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.79
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.58
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:21.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.77
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    1.39
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:22.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 9.71e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.51
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.89
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.87
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:01.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10048.20
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10053.97
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.044
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:34.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.94
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:45.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.57
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4016.93
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.07
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11740.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.91
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.58
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999925175

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.46
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000056908

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   0.097
p-value of test                       :    0.46

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:14.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 31  CouponCollector, r = 10         0.9999 
 58  AppearanceSpacings, r = 27      4.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 113737751.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:58.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:43.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:45.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:01.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:11.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:15.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.44
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    2.23
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     552
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:14.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.16
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:02:44.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.49
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.13
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.32
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.99
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.70
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.57
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.02
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:58.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.37
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:07.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7278.22
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.41
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:17.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.85
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  149.76
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:42.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4979.22
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:57.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45999
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869999
  j =  1                              :        399908006
  j =  2                              :            45991
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46387
p-value of test                       :  9.1e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870387
  j =  1                              :        399907230
  j =  2                              :            46379
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.45e-3
p-value of test                       :    0.9985

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:31.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:20.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:53.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:10.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 4.86e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.42e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.66e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:24.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:52.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.78
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.35
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.83
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.37
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9991    *****

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.78
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17258.62
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:51.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.62
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.58
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.41
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.01
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.62
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.62
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.90
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.84
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.50
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.64
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.20
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.16
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.44
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.43
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.79
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.89
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.29
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.76
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:42.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.43
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.58
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.52
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.34
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  240.19
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.26
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.73
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5182.96
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.06
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.81
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.43
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:20.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.79
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :  -0.060
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:19.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.00e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   24.20
p-value of test                       :  2.1e-3

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.31
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.00
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:02.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.80
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:01.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9967

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10146.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:04:24.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:57.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.09
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:00.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.96
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3923.43
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12150.52
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:37.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12128.72
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:39.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.88
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999910541

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.94
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999976964

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.19
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.3e-3

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:23.57

 All tests were passed




Server wird beendet - Lösche Semaphor 114753559.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1482
p-value of test                       :  8.6e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334602
  j =  1                              :        599997036
  j =  2                              :             1482
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5491
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:56.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:06.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:06.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:55.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:01.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:16.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:48.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.08
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.17
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.71
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.43
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.79
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.84
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.87
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.76
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.12
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1510.09
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7007.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:40.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   89.25
p-value of test                       :  8.5e-3

-----------------------------------------------
CPU time used                    :  00:03:00.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.25
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.79
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:33.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.47
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:53.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45865
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869865
  j =  1                              :        399908274
  j =  2                              :            45857
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45908
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869908
  j =  1                              :        399908190
  j =  2                              :            45896
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:27.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:16.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.84e-3
p-value of test                       :    0.9922

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:01:33.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.14e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.50e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.86e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.99
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.31
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.82
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:48.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.67
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.56
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.11
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.97
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17569.83
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.07
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.63
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.54
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.25
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.25
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.97
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.10
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.94
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.27
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.17
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.55
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.65
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.86
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.96
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.08
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.68
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.06
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.77
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.44
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.40
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.69
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.22
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.00
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.23
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.44
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.78
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.47
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.98
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  242.89
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.62
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:19.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.14
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:20.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
p-value of test                       :    0.9918

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.4e-3

Anderson-Darling statistic = A2       :    5.60
p-value of test                       :  1.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.27
p-value of test                       :  5.4e-4    *****

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    2.46
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.54e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 7.29e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.54
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.32
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.79
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:04.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:03.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9811.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10073.79
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:33.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.09
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.86
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:47.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3993.50
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.25
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11803.29
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.39
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.16
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999896024

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.17
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999960998

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:45.84
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  6  CollisionOver, t = 3            8.6e-4
 82  LempelZiv, r = 0                5.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 115769367.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5481
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:05.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:05.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:56.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:00.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.44
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    6.32
p-value of test                       :  7.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:16.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.23
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:44.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.01
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.88
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.75
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.14
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:43.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.45
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7026.78
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.62
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.70
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.83
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:35.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4890.11
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:55.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45684
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869684
  j =  1                              :        399908635
  j =  2                              :            45678
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45897
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869897
  j =  1                              :        399908209
  j =  2                              :            45891
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:27.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:17.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 9.02e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:55.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.42e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:37.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.37
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.09
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.33
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.43
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.47
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.57
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.35
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.31
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.40
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17498.84
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.39
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.69
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.97
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.15
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.78
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.23
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.47
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.68
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  101.34
p-value of test                       :    0.9981


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.14
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.85
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.93
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.77
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.72
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.68
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.98
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.63
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.17
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.44
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.70
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5242.61
p-value of test                       :  8.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.60
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.62
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.23
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.49
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.81
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  444.98
p-value of test                       :  9.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.73
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.16
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :   -2.31
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:20.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.17
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :    1.44
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:21.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 8.03e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.38e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.06
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.67
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.70
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:02.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:03.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10137.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.097
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:37.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.80
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:45.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4780.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:48.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4230.28
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.19
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.25
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000048979

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.27
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000050401

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:15.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP2S, t = 3         7.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 116785175.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5351
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:56.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:06.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:06.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7474
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:58.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:02.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.31
p-value of test                       :  6.3e-3

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    3.32
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:15.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:45.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.83
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.77
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   27.58
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  188.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.58
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1373.34
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6797.72
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.35
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   86.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:06.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.18
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.40
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:35.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5189.26
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:56.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45868
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869868
  j =  1                              :        399908267
  j =  2                              :            45862
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45591
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869591
  j =  1                              :        399908822
  j =  2                              :            45583
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:28.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:19.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:01.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:34.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.84e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 3.14e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 5.73e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.62
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.14
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.48
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:12.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.58
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.31
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.83
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17496.05
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.23
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.74
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   46.99
p-value of test                       :  4.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.32
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.12
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.58
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.87
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.39
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.14
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.99
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.58
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.44
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.63
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.67
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.64
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.41
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.46
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.19
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.04
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4866.33
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.64
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.82
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.22
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.08
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.58
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  435.58
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.10
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.75
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:22.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.74
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :    2.48
p-value of test                       :  6.6e-3



-----------------------------------------------
CPU time used                    :  00:02:24.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.01e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.97
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.84
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.03
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:02.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.45
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:04.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.31
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9951.19
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:35.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.96
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:45.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.86
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.06
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11937.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11557.38
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.66
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999848834

Normal statistic for number of bits   :   -1.20
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.40
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000114835

Normal statistic for number of bits   :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         : -4.40e-3
p-value of test                       :    0.50

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 4.36e-3
p-value of test                       :    0.9955

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:59.31

 All tests were passed




Server wird beendet - Lösche Semaphor 117800983.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1220
p-value of test                       : 1 -  3.8e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334340
  j =  1                              :        599997560
  j =  2                              :             1220
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5434
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:55.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:41.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4451
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:05.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:02.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:14.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.85
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:42.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.46
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.92
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.80
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.02
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.99
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.56
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.23
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.36
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6852.01
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.23
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.27
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:01.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.44
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.02
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:33.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5102.06
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:02.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46002
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870002
  j =  1                              :        399908000
  j =  2                              :            45994
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45891
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869891
  j =  1                              :        399908219
  j =  2                              :            45889
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:28.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:18.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:35.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 4.23e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.17
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.79
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.48
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.88
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.52
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.58
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:41.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.41
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.78
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.76e-4
p-value of test                       :    0.9993    *****

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  165.91
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17450.65
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.48
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.88
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.80
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.47
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.39
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.38
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.36
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.93
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.52
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.17
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.07
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.51
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.17
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.17
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.72
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.30
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.45
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.99
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.15
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.08
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.19
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.09
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.82
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.92
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.18
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.56
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.70
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.09
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    1.44
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:21.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.90
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:21.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    2.60
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.01e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.62e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.65
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.39
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-3
p-value of test                       :    0.9979

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  245.51
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:03.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:03.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9913.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.066
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:35.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4762.49
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4997.71
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4012.62
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.45
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.39
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.39
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000034204

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.38
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000057448

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    1.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:15.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14          1 -  3.8e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 118816791.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1475
p-value of test                       :  1.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334595
  j =  1                              :        599997050
  j =  2                              :             1475
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5359
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:55.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:06.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:06.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7485
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:55.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:04:01.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    4.66
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:15.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:44.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.29
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.14
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.72
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.87
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.73
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.78
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.37
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.18
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.19
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.30
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7120.79
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.76
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:02.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.47
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.57
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4925.98
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:01.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45521
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869521
  j =  1                              :        399908964
  j =  2                              :            45509
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46012
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870012
  j =  1                              :        399907978
  j =  2                              :            46008
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:28.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:18.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:59.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.85e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:35.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.85
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.52
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.34
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.32
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.67
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.00
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.76
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:40.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.77
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.57
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17462.94
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.37
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.68
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.77
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.42
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.34
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.01
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.71
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.09
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.98
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.02
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.45
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.52
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.22
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.88
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.60
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.84
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.25
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.43
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.03
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.44
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.34
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.49
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.37
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5135.28
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.77
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.84
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.14
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.17
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    2.15
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:21.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.65e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.03e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.68
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.91
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.14
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:03.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:04.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.91
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10131.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.25
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:35.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5071.32
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:45.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.00
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4204.69
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11598.07
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11910.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.91
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000085552

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.63
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999821849

Normal statistic for number of bits   :   -1.41
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.76
p-value of test                       :    0.04

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.81
p-value of test                       :    0.04

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:59.65

 All tests were passed




Server wird beendet - Lösche Semaphor 119832599.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5351
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:54.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4231
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:06.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:55.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:01.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.17
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    2.39
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     953
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:15.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:42.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.13
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.01
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.55
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.09
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.47
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.15
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.61
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.83
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.63
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.36
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7205.47
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:41.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:02.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.35
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.79
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4983.57
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:02.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45934
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869934
  j =  1                              :        399908136
  j =  2                              :            45926
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45736
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869736
  j =  1                              :        399908532
  j =  2                              :            45728
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:28.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9916

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:18.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:54.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:33.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.58e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:38.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.13
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:48.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.54
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.16
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.78
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:41.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.90
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.09
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.47
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.94
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17620.71
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.68
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.24
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.60
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.87
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.31
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.07
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.49
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.12
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.69
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.02
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.82
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.16
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.32
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.64
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.90
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.05
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.14
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.34
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.46
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.91
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4854.50
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.53
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.90
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.58
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.82
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.14
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.55
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.26
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.00
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:23.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.98
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:21.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.58e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.87e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 9.05e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.47
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.61
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:03.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.73
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:03.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.90
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10184.77
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:37.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.80
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.17
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.17
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.23
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12065.04
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.75
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000166201

Normal statistic for number of bits   :    1.31
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.13
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999913682

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
p-value of test                       :    0.9903

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   0.044
p-value of test                       :    0.48

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:42.35

 All tests were passed




Server wird beendet - Lösche Semaphor 120848407.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:50.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1266
p-value of test                       :    0.9963

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334386
  j =  1                              :        599997468
  j =  2                              :             1266
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5380
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:56.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:44.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:01.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4200
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:02.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:14.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:11.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:15.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.42
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.23
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:13.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:44.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.11
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.14
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.80
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.70
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.26
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.79
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:02.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7204.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.26
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:19.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.45
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.43
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4987.29
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:53.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45684
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869684
  j =  1                              :        399908639
  j =  2                              :            45670
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46414
p-value of test                       :  6.4e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870414
  j =  1                              :        399907176
  j =  2                              :            46406
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:24.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :  2.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:11.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:59.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:51.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:33.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.45e-5
p-value of test                       :    0.9916

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.43e-5
p-value of test                       :    0.9919

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:43.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:43.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   40.66
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.25
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.15
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.15
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.30
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.17
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.90
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.55
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17562.47
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:47.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.88
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.59
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.51
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.36
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.91
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.33
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.45
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.09
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.86
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.78
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  100.20
p-value of test                       :    0.9908


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.63
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.06
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.07
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.45
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.42
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.65
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.62
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.59
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.94
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.87
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.47
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:31.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.32
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4819.51
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.63
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.59
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:32.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.17
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:09.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.02
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:09.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.53e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:40.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.35
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.80
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.56
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:53.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:53.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10074.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9702.84
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:04:01.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.10
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.61
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.25
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.17
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11770.65
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11962.68
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:29.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.64
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000015448

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.23
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000118453

Normal statistic for number of bits   :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:34.19

 All tests were passed




Server wird beendet - Lösche Semaphor 121864215.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5433
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:42.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4480
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:34.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:54.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:54.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:00.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:01.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:52.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:58.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.28
p-value of test                       :  6.7e-3

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:11.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9948


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    3.13
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:36.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.39
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.06
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.90
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.09
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.60
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1502.45
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7141.73
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.65
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.08
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:03.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.69
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.14
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:35.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5056.83
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:11.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45756
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869756
  j =  1                              :        399908490
  j =  2                              :            45752
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46314
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870314
  j =  1                              :        399907376
  j =  2                              :            46306
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:29.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  6.7e-3

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:17.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:44.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:52.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 8.35e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:35.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:48.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.08
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.97
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.12
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.76
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.76
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.99
p-value of test                       :  3.1e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   19.33
p-value of test                       :    0.9976

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.61
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.52
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.98
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:40.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17182.14
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.65
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.40
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.45
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.24
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.38
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.71
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.15
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.88
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.23
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.63
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.85
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.29
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.99
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.39
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.91
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.22
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.49
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.94
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.58
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.63
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.21
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5108.49
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.08
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.05
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.82
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.49
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.00
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  322.93
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.15
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.84
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:16.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.95
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:23.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:12.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.10e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.81e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 7.16e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.08
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.57
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.97
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:08.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.78
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:07.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.77
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10096.64
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:43.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5047.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.86
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11806.92
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12053.13
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:29.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.72
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999978227

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.89
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999947408

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:14:36.71

 All tests were passed




Server wird beendet - Lösche Semaphor 102367256.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5183
p-value of test                       :    0.9994    *****


-----------------------------------------------
CPU time used                    :  00:03:45.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:37.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:35.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:54.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:54.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:01.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:02.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:52.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:57.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    3.06
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     853
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:45.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.94
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:11.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.46
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:42.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    5.72
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.51
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.07
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.18
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.84
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.05
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  179.34
p-value of test                       :    0.9957

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.75
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.65
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7106.72
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.01
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.08
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:05.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.42
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.62
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:35.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5103.30
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45923
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869923
  j =  1                              :        399908159
  j =  2                              :            45913
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869769
  j =  1                              :        399908465
  j =  2                              :            45763
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:28.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:17.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:53.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 2.83e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.20e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.080
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:38.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:37.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.82
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:47.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.02
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.09
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:47.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.12
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.90
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.73
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.99
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.98
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17248.43
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:52.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.05
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.99
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.06
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.91
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.68
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.88
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.59
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.64
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.49
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.65
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.75
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.31
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.36
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.96
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.52
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.53
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.27
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.57
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.55
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.82
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5113.17
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.01
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.95
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.09
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.07
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5081.81
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.76
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.35
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:34.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.55
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   0.079
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:23.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.72
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:26.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.71e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:46.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 4.95e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.55
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.40
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.09
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:04.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:05.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  2.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    4.27
p-value of test                       :  6.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9659.35
p-value of test                       :    0.9925

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9859.18
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:04:04.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5020.08
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:48.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.55
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4016.09
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11960.15
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.50
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.65
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000062722

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.99
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000079789

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:58.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 13  BirthdaySpacings, t = 2         0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 103088152.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:52.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1475
p-value of test                       :  1.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334595
  j =  1                              :        599997050
  j =  2                              :             1475
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5272
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:46.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:37.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:37.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4501
p-value of test                       :  6.7e-3


-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:01.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:02.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:53.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:57.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    4.35
p-value of test                       :  5.9e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     968
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    3.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:03.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     557
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.14
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    2.37
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     255
p-value of test                       :    0.9957

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:17.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:44.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.21
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.18
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.54
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.16
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.18
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.18
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.65
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:58.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7095.56
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.34
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.58
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.85
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:35.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.53
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45966
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869966
  j =  1                              :        399908070
  j =  2                              :            45962
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45747
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869747
  j =  1                              :        399908508
  j =  2                              :            45743
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:28.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:21.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:48.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.7e-3

Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
p-value of test                       :    0.9910

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9915


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:02.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:53.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
p-value of test                       :    0.9905

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.63e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.19e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.043
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:37.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.09
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:47.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.42
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.19
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.48
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.01
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:43.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.00
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.70
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    3.70
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17206.39
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.91
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.49
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.16
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.83
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.80
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.72
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.50
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.72
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.29
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.03
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.12
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.51
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.87
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.22
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.55
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.62
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.63
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.86
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.80
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.68
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5219.39
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.29
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.31
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.51
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.94
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4843.48
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.34
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.72
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.28
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :    2.02
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:26.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.96
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    1.37
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:47.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.06
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.27
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9981

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.58
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:06.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.24
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:09.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9857.47
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.66
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:04:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4726.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:50.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.75
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.40
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11768.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11651.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.86
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000122548

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.32
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999970901

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :  -0.080
p-value of test                       :    0.53

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:21.60

 All tests were passed




Server wird beendet - Lösche Semaphor 104071192.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5332
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:47.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:35.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:53.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:55.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:03.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:03.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:53.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:55.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.37
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:14.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.04
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:02:43.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.97
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.75
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.77
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  190.71
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7102.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:09.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.52
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.73
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5044.85
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:05.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45839
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869839
  j =  1                              :        399908324
  j =  2                              :            45835
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46028
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870028
  j =  1                              :        399907951
  j =  2                              :            46014
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:30.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:17.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :  2.5e-3

Anderson-Darling statistic = A2       :    4.45
p-value of test                       :  5.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:45.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:03.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:57.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 3.10e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.049
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.53
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.65
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.10
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.38
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.19
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.98
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.09
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.53
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17244.56
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.62
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.43
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.42
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.86
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.74
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.53
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.64
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.33
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.07
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.15
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.42
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.33
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.64
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.54
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.51
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.51
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.57
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.41
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.33
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.27
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.55
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.50
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4808.21
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.74
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.61
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.50
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.23
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4812.19
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.14
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.74
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.55
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:22.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.85
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:22.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.060
p-value of test                       :    0.52

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.11e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.21
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.72
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.41
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:08.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.97
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:07.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.89
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10126.88
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:04:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:53.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4755.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:54.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.39
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.02
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.51
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11982.75
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:31.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.35
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999825320

Normal statistic for number of bits   :   -1.38
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.57
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999929852

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:40.20

 All tests were passed




Server wird beendet - Lösche Semaphor 105054232.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997359
  j =  2                              :             1319
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5503
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:49.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:39.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:05.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:03.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:01.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:05.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    2.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    2.71
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:13.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.26
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.15
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.88
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.35
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.68
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.45
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.26
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.13
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:57.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.69
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:05.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7022.51
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.59
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.03
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:16.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.61
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.13
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5145.45
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:09.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45948
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869948
  j =  1                              :        399908105
  j =  2                              :            45946
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908188
  j =  2                              :            45903
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:31.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:20.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:49.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:05.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.13e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.087
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.11
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.12
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.31
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.05
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.09
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:51.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.39
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.79
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17479.13
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.25
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.38
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.88
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.97
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.59
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.39
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.45
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.23
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.30
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.18
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.97
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.07
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.14
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.03
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.11
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.64
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.47
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.88
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.52
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.31
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4828.91
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.74
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.32
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.08
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.23
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.23
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.12
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.86
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.21
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:25.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.94
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:23.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 7.41e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.66
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.09
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.90
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:06.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-3
p-value of test                       :    0.9976

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:09.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10137.41
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9859.38
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.095
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:04:28.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.27
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3965.46
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12068.18
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11504.44
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:36.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.12
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000135424

Normal statistic for number of bits   :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.52
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000004687

Normal statistic for number of bits   :   0.037
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.91
p-value of test                       :    0.03

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.73

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:02.61

 All tests were passed




Server wird beendet - Lösche Semaphor 106233880.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:48.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:38.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:37.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7125
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:04.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:56.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:01.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:12.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:42.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.75
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.30
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.47
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.64
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.88
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.05
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  385.57
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1582.85
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:02:00.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7166.37
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.09
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9927

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.90
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:01.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.36
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.65
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5160.50
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:58.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908145
  j =  2                              :            45923
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45800
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869800
  j =  1                              :        399908404
  j =  2                              :            45792
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:26.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:15.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:01.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.41e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.91e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.41
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.59
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.50
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.75
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.75
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   11.35
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.46
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 7.44e-3
p-value of test                       :    0.9920

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17783.67
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.37
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.45
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.34
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.22
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.61
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.68
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.84
p-value of test                       :    0.9937


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.67
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.80
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.69
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.05
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.82
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.85
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.09
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.01
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.32
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.34
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.15
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.12
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.77
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.22
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5180.63
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.70
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.78
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.57
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.16
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.08
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.30
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.47
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.53
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -1.93
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:23.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.70
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.08

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.95
p-value of test                       :    0.03

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 7.60e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 7.21e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9923

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.29
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.60
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  248.50
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:08.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.85
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:09.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10135.84
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10285.91
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:43.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.73
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:49.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.41
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:51.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4022.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.55
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.52
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11591.61
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.89
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000167221

Normal statistic for number of bits   :    1.32
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.93
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000013279

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9902

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:34.68

 All tests were passed




Server wird beendet - Lösche Semaphor 107446296.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5527
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:49.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:37.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:03.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:04.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:55.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:00.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    3.45
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.74
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.67
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:12.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:43.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.32
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.94
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.39
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.90
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.23
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.35
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.11
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1504.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6989.91
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:03.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.69
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.80
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5004.07
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:15.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45599
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869599
  j =  1                              :        399908804
  j =  2                              :            45595
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45661
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869661
  j =  1                              :        399908683
  j =  2                              :            45651
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:26.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:18.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  2.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    4.39
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:01:53.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.16e-3
p-value of test                       :    0.9918

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:33.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.57e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.097
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:46.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.87
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:47.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.66
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.76
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.34
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.11
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.17
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 2.84e-3
p-value of test                       :    0.9971

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.85
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.59
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.22
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.88
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17330.59
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.38
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.32
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.65
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.19
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.87
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.31
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.86
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.74
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.38
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.27
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.47
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.95
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.57
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.70
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.03
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :   99.69
p-value of test                       :    0.9988


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.05
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.97
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.78
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.41
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.15
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.63
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.39
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.55
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.29
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.77
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.59
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.19
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.67
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.13
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.89
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    1.10
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:22.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.3e-3

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.32e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.30
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.88
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.06
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:07.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.97
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:08.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9669.15
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9798.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:40.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4773.25
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.17
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:50.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.52
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.91
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11999.85
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.40
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999961886

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.45
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000043195

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.16
p-value of test                       :    0.9974

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         : -8.28e-3
p-value of test                       :    0.50

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:45.30

 All tests were passed




Server wird beendet - Lösche Semaphor 108429336.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:42.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:52.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:39.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:38.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:03.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:54.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7583
p-value of test                       :  1.1e-3


-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9952

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    2.61
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:13.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:47.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.77
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.98
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.72
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.62
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.59
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.59
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.50
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:43.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.30
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:59.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6956.46
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.84
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:08.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.65
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5025.57
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:54.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45166
p-value of test                       :    0.9996    *****


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869166
  j =  1                              :        399909669
  j =  2                              :            45164
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45964
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869964
  j =  1                              :        399908074
  j =  2                              :            45960
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:27.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:17.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:43.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.29e-4
p-value of test                       :    0.9992    *****

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:32.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.21e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.68e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.084
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.041
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:36.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.03
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.95
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.11
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.01
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:40.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.09
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17153.23
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.58
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.87
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.97
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.70
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.98
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.79
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.85
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.53
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.45
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.86
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.85
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.25
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.52
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.79
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.01
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.38
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.88
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.18
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.77
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.64
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.71
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.34
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.41
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.92
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.26
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.21
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    1.77
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:22.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.19
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    1.55
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:24.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.66e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.93e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 9.50e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   22.42
p-value of test                       :  4.2e-3

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.83
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  244.81
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:06.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:08.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.57
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10170.70
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:43.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.13
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.12
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:50.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4301.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.96
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11969.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12068.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.31
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000045466

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.89
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999985031

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:07.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 44  CollisionPermut, r = 0          0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 109314072.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:52.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:03.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:04.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:54.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7166
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:00.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    2.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    2.42
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     267
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    2.33
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:13.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:40.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.94
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.45
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.90
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.41
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.95
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:43.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.65
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6889.74
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.47
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:02.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.24
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.79
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:33.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5015.06
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:58.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45980
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869980
  j =  1                              :        399908047
  j =  2                              :            45966
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46174
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870174
  j =  1                              :        399907654
  j =  2                              :            46170
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:27.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:18.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:54.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:32.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.66e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.31e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.079
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.92
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.98
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.74
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.11
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:47.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.42
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.13
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.49
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.18
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17389.02
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.09
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.78
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.53
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.23
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.29
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.04
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.76
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.40
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.59
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.28
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.20
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.56
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.13
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.28
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.45
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.93
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.61
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.43
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.58
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.12
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.96
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.43
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.13
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.42
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.08
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.79
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.43
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.88
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.64
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   -1.77
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.57
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   0.021
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:24.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 8.87e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.77
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.97
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:05.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:07.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9967.44
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:41.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4762.75
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:47.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.94
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4267.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.04
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11930.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11927.29
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.16
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999992042

Normal statistic for number of bits   :  -0.063
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.37
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999956615

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.63
p-value of test                       :    0.05

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:52.01

 All tests were passed




Server wird beendet - Lösche Semaphor 110264344.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5467
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:53.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4156
p-value of test                       :    0.9971


-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:57.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:05.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:05.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7509
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:57.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:00.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.01
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:45.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:11.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.63
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.25
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.20
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.55
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.32
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.90
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.05
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:06.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6945.97
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.17
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:07.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.09
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.18
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5121.18
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:56.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45551
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869551
  j =  1                              :        399908898
  j =  2                              :            45551
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45584
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869584
  j =  1                              :        399908838
  j =  2                              :            45572
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:29.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:17.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:36.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.16e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 7.90e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:39.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.28
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.50
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.28
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:45.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.05
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.37
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17516.59
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.09
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.29
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.88
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.61
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.86
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.50
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.78
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.13
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.93
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.92
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.92
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.91
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.25
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.65
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.96
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.11
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.19
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.86
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.54
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.20
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.37
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.34
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.07
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.76
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.45
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.19
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5100.55
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.53
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.56
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.21
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:24.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.60
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    0.37
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:24.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 2.29e-3
p-value of test                       :    0.9977

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -2.08
p-value of test                       :    0.98

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.72e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 8.45e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.83e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.50
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.11
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:05.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.38
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9890.34
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.15
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:04:12.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4791.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:51.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4749.70
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:53.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4249.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.92
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11817.38
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.91
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000157468

Normal statistic for number of bits   :    1.24
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.74
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999999254

Normal statistic for number of bits   : -5.90e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.66

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:10.72

 All tests were passed




Server wird beendet - Lösche Semaphor 111247384.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5433
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:53.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4451
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:57.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:07.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:07.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:00.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:03.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.36
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:13.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.94
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.72
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    4.48
p-value of test                       :  5.1e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     178
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:38.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.93
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.63
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.01
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.91
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.57
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.93
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1469.47
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:04.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7143.31
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:53.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   49.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.06
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.75
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   88.20
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5095.01
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:58.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46021
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870021
  j =  1                              :        399907961
  j =  2                              :            46015
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46071
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870071
  j =  1                              :        399907863
  j =  2                              :            46061
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  9.5e-3

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:30.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:18.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:05.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 6.10e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.058
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:43.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:44.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.74
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.48
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.30
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.66
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   61.93
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.24
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.84
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.73
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.84
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.63
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17557.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.09
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.17
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.85
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.57
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.55
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.31
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.67
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.18
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.96
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.55
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.34
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.93
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.54
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.11
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.92
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.81
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.99
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.01
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.98
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.52
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.64
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.58
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5085.53
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.73
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.60
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.43
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.06
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.05
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.82
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.35
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.53
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.93
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.06e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.38
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.38
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.22
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:05.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.12
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.04
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10167.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.077
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:04:19.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.24
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:53.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4757.72
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.13
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.59
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11457.33
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11926.10
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:32.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.94
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000011692

Normal statistic for number of bits   :   0.092
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.13
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999942869

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:08.95

 All tests were passed




Server wird beendet - Lösche Semaphor 112230424.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5436
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:51.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7471
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:40.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4512
p-value of test                       :  4.2e-3


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:05.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7122
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:01.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     856
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     271
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:15.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    2.56
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:42.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.07
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.40
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.70
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.18
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.83
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.26
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.38
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1401.42
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6974.82
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:41.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.25
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.77
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:02.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.40
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.41
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:33.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5024.14
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:57.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46014
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870014
  j =  1                              :        399907978
  j =  2                              :            46002
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908340
  j =  2                              :            45824
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:26.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:18.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:01.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 9.28e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:32.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:32.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.73
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.52
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:40.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.36
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.46
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17541.47
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.45
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.42
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.66
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.14
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.71
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.05
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.56
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.14
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   35.74
p-value of test                       :  5.0e-3


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.63
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.55
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.64
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  170.38
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.01
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.33
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.10
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  563.00
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.20
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.32
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.55
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.99
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4869.25
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.07
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.56
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.30
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.02
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.69
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.40
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.93
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.12
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.60
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:24.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.61e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.20
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.01
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.76
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.50
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:05.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9845.32
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9865.69
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:38.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4814.90
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.56
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:50.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4188.69
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4046.17
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11927.46
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11959.68
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:30.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.88
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999750254

Normal statistic for number of bits   :   -1.97
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.43
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000032026

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:32.22

 All tests were passed




Server wird beendet - Lösche Semaphor 113377304.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5374
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:53.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7529
p-value of test                       :  7.2e-3


-----------------------------------------------
CPU time used                    :  00:02:39.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4218
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:03.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:03.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:54.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:59.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     960
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:45.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    2.01
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:12.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.86
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    2.50
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:43.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.88
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.20
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.39
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.60
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.09
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.46
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:43.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.60
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:01.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7053.35
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:41.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.81
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:04.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.60
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:47.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.20
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4880.93
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:54.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45614
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869614
  j =  1                              :        399908775
  j =  2                              :            45608
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46085
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870085
  j =  1                              :        399907835
  j =  2                              :            46075
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:27.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:20.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:46.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:56.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:33.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 6.87e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 2.88e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:34.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.83
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:01:34.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.93
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.78
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.28
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.40
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.22
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.97
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.28
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9947

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.19
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.47
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.45
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17345.56
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.79
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.30
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.78
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.91
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.18
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.22
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.69
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.53
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.59
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.60
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.03
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.61
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.54
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.13
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.61
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.11
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.85
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.92
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.89
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.77
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.03
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.43
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  435.88
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.33
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.04
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.45
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.77
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.01
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.44
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.79
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.63
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 7.99e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.62e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 4.59e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.06
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.31
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.75
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:06.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.43
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:05.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9774.83
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10132.98
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.50
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:03:41.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.09
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.31
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.33
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.56
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11666.38
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.24
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000055066

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.91
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999995633

Normal statistic for number of bits   :  -0.035
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:50.62

 All tests were passed




Server wird beendet - Lösche Semaphor 114327576.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:48.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:04.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:03.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:53.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:58.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    3.68
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:11.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:38.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.37
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.13
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.23
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.25
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.67
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.07
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7065.09
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:41.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.21
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.83
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.69
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:33.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5123.54
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:56.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45810
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869810
  j =  1                              :        399908385
  j =  2                              :            45800
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45908
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869908
  j =  1                              :        399908185
  j =  2                              :            45906
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:26.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.72e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 3.25e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 8.18e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.074
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.02
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.22
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.66
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:48.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.92
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.66
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.86
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.48
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17211.13
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.09
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.00
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.31
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.59
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.04
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.34
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.07
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.52
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.27
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.68
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.60
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.49
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.61
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.01
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.31
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.65
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.27
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.48
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.93
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.91
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.93
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.39
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.88
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.36
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.58
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.89
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.08
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.46
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.43
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.80
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.54
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:22.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 4.87e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.84
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.01
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.63
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:05.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.39
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9833.98
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.76
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:37.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.13
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.14
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11700.32
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12047.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.24
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000025033

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.47
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000011989

Normal statistic for number of bits   :   0.095
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:17.12

 All tests were passed




Server wird beendet - Lösche Semaphor 115212312.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5503
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:55.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:41.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:06.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7494
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:54.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:59.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:12.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    6.28
p-value of test                       :  8.3e-4    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.07
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.66
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.99
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.34
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.70
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.77
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.36
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1369.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:01.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7038.66
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.02
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.44
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:03.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.04
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.15
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4973.15
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:58.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45804
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869804
  j =  1                              :        399908392
  j =  2                              :            45804
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46190
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870190
  j =  1                              :        399907627
  j =  2                              :            46176
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:28.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:19.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.07e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:34.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:34.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.83
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.74
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.77
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.67
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:43.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.1e-3

Anderson-Darling statistic = A2       :    3.74
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17131.17
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.70
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.43
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.88
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.00
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.04
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.10
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.25
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.52
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.72
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.55
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.24
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  440.99
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.30
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.93
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.00
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.33
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.07
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.18
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.32
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.62
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5136.51
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.88
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.80
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.04
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.38
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.64
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.58
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  242.14
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.98
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :    1.24
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:21.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.67
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:21.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :  -0.098
p-value of test                       :    0.54

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.28e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.29e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.26
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.70
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.77
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:06.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:05.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9891.19
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9969.87
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.048
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:40.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.77
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.20
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:50.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3950.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11736.40
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12061.16
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.25
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000045553

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.99
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000098263

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:11.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs NP, t = 16           8.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 116228120.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:49.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:56.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7174
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:07.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:05.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:56.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:58.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.38
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.26
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    2.00
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     642
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.46
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:13.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.65
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    2.22
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.17
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.97
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.91
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.06
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:43.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.09
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:02.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6795.82
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:45.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:06.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.90
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.25
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.85
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:55.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45777
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869777
  j =  1                              :        399908449
  j =  2                              :            45771
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46192
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870192
  j =  1                              :        399907625
  j =  2                              :            46174
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:28.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.65e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.044
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.29
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.10
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.86
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9931

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17484.09
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.02
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.61
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.87
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.83
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.77
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.87
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.36
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.87
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.21
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.33
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.23
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.45
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.26
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.14
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.23
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.34
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.23
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.71
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.77
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.51
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.22
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5052.87
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.02
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.83
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.74
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.66
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.70
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.04
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.38
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.56
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :    1.10
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.00
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :  -0.091
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.18
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.85e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 6.31e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.72e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 9.29e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.84
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.67
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:04.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.80
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10133.48
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:58.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:50.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5025.55
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:51.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.83
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11523.56
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11871.00
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:30.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   31.58
p-value of test                       :    0.9937


-----------------------------------------------
Total number of bits:  7999976289

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.48
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000037831

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:31.97

 All tests were passed




Server wird beendet - Lösche Semaphor 117211160.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5463
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:57.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4218
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:05.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:04.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:55.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:00.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:13.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:38.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.84
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.37
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.85
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.86
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.46
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:44.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:01.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6913.54
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.04
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.57
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:04.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.58
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  156.54
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5040.14
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:58.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45915
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869915
  j =  1                              :        399908173
  j =  2                              :            45909
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46076
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870076
  j =  1                              :        399907851
  j =  2                              :            46070
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:27.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:18.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 5.07e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.31
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:48.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.19
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.75
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.24
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.29
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17613.24
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.46
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.29
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.86
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.91
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.47
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.82
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.38
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.66
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.39
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.35
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.71
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.50
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.86
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.63
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.08
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.20
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.01
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.98
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.52
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.37
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  444.38
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4818.17
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.14
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.38
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.19
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4777.90
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.38
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.53
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    1.44
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:23.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.19
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:21.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         : -5.43e-3
p-value of test                       :    0.50

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.09e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.92e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 7.95e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.69
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.29
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.69
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:07.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10145.88
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.69
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.37
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:03:39.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.12
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.34
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4022.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.21
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.49
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11799.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.38
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999935138

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.47
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000027961

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    2.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:20.07

 All tests were passed




Server wird beendet - Lösche Semaphor 118226968.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5479
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:57.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:05.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:05.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:55.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:00.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.44
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    3.14
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:13.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9922


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.05
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    2.57
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.25
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.44
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.29
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.64
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.39
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.99
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.65
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.53
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  188.78
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  480.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.52
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7201.47
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.86
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:03.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  151.77
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:33.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4969.08
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:58.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46294
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870294
  j =  1                              :        399907419
  j =  2                              :            46280
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46040
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870040
  j =  1                              :        399907925
  j =  2                              :            46030
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:27.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    5.02
p-value of test                       :  2.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9980


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:19.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:02.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:55.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.9999    *****

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.98e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -5.92e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.75
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:47.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.74
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.49
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.15
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.21
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.96
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.50
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.83
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17462.54
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.79
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.75
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.14
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.29
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.89
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.39
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.10
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.30
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.44
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.40
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.25
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.34
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.25
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.00
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.50
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.81
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.44
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.11
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.23
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.61
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.45
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4788.03
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.52
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.45
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.36
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.94
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.50
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.84
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.08
p-value of test                       :    0.9949


-----------------------------------------------
Normal statistic for number of jumps  :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.07
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:22.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 6.22e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.22
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.46
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:07.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.092
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:38.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.41
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.15
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:51.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.35
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.26
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11785.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.74
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:29.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.17
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999861125

Normal statistic for number of bits   :   -1.10
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.64
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999826172

Normal statistic for number of bits   :   -1.37
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.24
p-value of test                       :    0.99

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.94
p-value of test                       :    0.97

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:25.94

 All tests were passed




Server wird beendet - Lösche Semaphor 119242776.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5368
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:58.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:06.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:55.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:00.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.45
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:14.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:42.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.56
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.40
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.41
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.76
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.42
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.33
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.47
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.40
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7264.49
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.25
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.44
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:05.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.83
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.31
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5036.44
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:57.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45696
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869696
  j =  1                              :        399908610
  j =  2                              :            45692
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45850
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869850
  j =  1                              :        399908305
  j =  2                              :            45840
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:28.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:19.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:03.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:54.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.05e-3
p-value of test                       :    0.9919

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.80e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.077
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.076
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:47.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.80
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.29
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.08
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:42.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.31
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.66
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17308.26
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.52
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.81
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.25
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.73
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.54
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.68
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.63
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.58
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.70
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.56
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.43
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.69
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.13
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.11
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.90
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.10
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.12
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.99
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.76
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.27
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.80
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.32
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.79
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.05
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.33
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.29
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.99
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.97
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.30
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.52
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   0.043
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:23.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.84
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 8.73e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.35
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.22
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.98
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:04.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.94
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:05.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10060.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.47
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:40.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5050.41
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:51.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3977.89
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.32
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.50
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11995.45
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.67
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999971192

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.65
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999995645

Normal statistic for number of bits   :  -0.034
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         : -4.12e-3
p-value of test                       :    0.50

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.3e-3

Anderson-Darling statistic = A2       :    4.72
p-value of test                       :  4.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.53
p-value of test                       :  5.6e-3

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:56.75

 All tests were passed




Server wird beendet - Lösche Semaphor 120225816.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5413
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:01.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:43.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7084
p-value of test                       :    0.9970


-----------------------------------------------
CPU time used                    :  00:02:45.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:02.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:12.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:11.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:08.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:09.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.10
p-value of test                       :  7.9e-3

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:13.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.03
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.98
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.36
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.88
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.14
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.20
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:54.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1562.16
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:06.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7190.34
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.17
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:15.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.78
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.17
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5006.60
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:59.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45961
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869961
  j =  1                              :        399908080
  j =  2                              :            45957
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45995
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869995
  j =  1                              :        399908016
  j =  2                              :            45983
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:32.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:07.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:57.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 5.74e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.084
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:52.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.64
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.17
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.11
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.09
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.72
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.84
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.6e-3

Anderson-Darling statistic = A2       :    3.92
p-value of test                       :  1.0e-2

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   67.48
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.77
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.47
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.03
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17810.81
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:51.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.59
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.56
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.98
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.55
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.70
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.94
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.62
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.35
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.66
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.30
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.35
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.69
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.40
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.79
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.34
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.07
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.93
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.37
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.23
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.36
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.61
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.34
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.49
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  243.79
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.62
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.98
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4891.97
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.01
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.91
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.15
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    1.26
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:20.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.70
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -1.49e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:20.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.31e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.80
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.08
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.82
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:00.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.84
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9964.42
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.045
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:04:05.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.76
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.80
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:51.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.47
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4231.34
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11968.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12054.06
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.22
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999860744

Normal statistic for number of bits   :   -1.10
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.03
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999993950

Normal statistic for number of bits   :  -0.048
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.96e-3
p-value of test                       :    0.9915

Anderson-Darling statistic = A2       :    4.18
p-value of test                       :  7.5e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.70
p-value of test                       :    0.9965

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:49.84

 All tests were passed




Server wird beendet - Lösche Semaphor 121208856.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1259
p-value of test                       :    0.9979

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334379
  j =  1                              :        599997482
  j =  2                              :             1259
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:41.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:36.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:34.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4220
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:54.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:00.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:00.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:53.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7158
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:58.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    3.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.86
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:11.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.42
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    4.13
p-value of test                       :  7.6e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:33.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.24
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.63
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.27
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.68
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.90
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.74
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1409.89
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:01.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7221.82
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.43
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.93
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:02.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.04
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.88
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5105.34
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:11.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45790
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869790
  j =  1                              :        399908426
  j =  2                              :            45778
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45989
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869989
  j =  1                              :        399908026
  j =  2                              :            45981
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:28.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:18.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9937


-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:58.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:53.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:35.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.97e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.69e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.051
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:34.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:34.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.53
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.83
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.59
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.64
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.82
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:40.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17695.10
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.78
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.11
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.95
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.41
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.02
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.03
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.57
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.14
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   35.13
p-value of test                       :  6.0e-3


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.02
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.84
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.10
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.00
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.67
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.87
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.50
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.93
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.76
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.58
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.75
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.19
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:34.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.64
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.50
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4845.90
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.60
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.45
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:33.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.31
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:16.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.97
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:21.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.58e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:46.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.80e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.61
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.84
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.36
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:08.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.23
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:07.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10123.70
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.95
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:43.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4760.12
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4814.30
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:49.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4236.13
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11728.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12044.28
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.51
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000099667

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.56
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000122692

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.05

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:14:15.93

 All tests were passed




Server wird beendet - Lösche Semaphor 102400025.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:52.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1466
p-value of test                       :  3.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334586
  j =  1                              :        599997068
  j =  2                              :             1466
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:44.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:35.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4214
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:54.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:02.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:02.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:53.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:59.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    2.75
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:10.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:36.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.94
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.89
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.41
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.34
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.00
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.42
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1618.35
p-value of test                       :  5.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7257.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:43.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.64
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.05e-3
p-value of test                       :    0.9989

Anderson-Darling statistic = A2       :    4.04
p-value of test                       :  8.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   33.42
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:03:03.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.48
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.93
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:35.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5177.71
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:02.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45673
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869673
  j =  1                              :        399908656
  j =  2                              :            45669
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45997
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869997
  j =  1                              :        399908009
  j =  2                              :            45991
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:28.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:17.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:57.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.88e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.79e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.96
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:47.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.04
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.62
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   46.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:41.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.59
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.99
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.03e-3
p-value of test                       :    0.9914

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.23
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17180.26
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.57
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.07
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.78
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.03
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.06
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.82
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.42
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.13
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.39
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.62
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.93
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.62
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.55
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.75
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.49
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.41
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.74
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.94
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.42
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.24
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.55
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.35
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.16
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:34.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.60
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.83
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.11
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.86
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.26
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.68
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    3.29
p-value of test                       :  5.1e-4    *****



-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.10
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:20.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.87e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 5.45e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.91e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.74
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.95
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.88
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:08.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.26
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:06.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9860.12
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
p-value of test                       :    0.9910

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9685.49
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:47.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.22
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.93
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.96
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11800.91
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11847.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.63
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999944246

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.13
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000136987

Normal statistic for number of bits   :    1.08
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:50.82
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 36  Gap, r = 0                      5.5e-4
 80  LinearComp, r = 0               5.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 103055385.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:52.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5392
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:46.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4456
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:37.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:35.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:53.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4471
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:01.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:02.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:55.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:56.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:14.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.81
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.53
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    4.86
p-value of test                       :  3.3e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     176
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:41.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.63
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.56
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.64
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.05
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.18
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.43
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.90
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.97
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.04
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:06.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7056.34
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.84
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.41
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:09.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.44
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.14
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5131.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45962
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869962
  j =  1                              :        399908080
  j =  2                              :            45954
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45886
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869886
  j =  1                              :        399908233
  j =  2                              :            45876
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:30.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:45.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :  1.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:01.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:36.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 9.94e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.055
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.93
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.87
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.88
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.26
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.69
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.71
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.03
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17676.43
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.26
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.27
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.89
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.20
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.85
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.25
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.49
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.56
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.47
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.38
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.60
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.25
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.23
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.47
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.18
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.91
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.05
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.98
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  453.29
p-value of test                       :  8.5e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.76
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.79
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.92
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.87
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.41
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5146.06
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.93
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.20
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.86
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:24.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.04
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:25.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.26e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.52e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.13
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.28
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.40
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:09.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10038.52
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.85e-3
p-value of test                       :    0.9949

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10357.82
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.75
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:04:21.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:53.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.80
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:53.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.85
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.58
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.37
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:32.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.51
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:31.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.88
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000053356

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.16
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999903809

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:11.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :  -0.058
p-value of test                       :    0.52

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:53.04

 All tests were passed




Server wird beendet - Lösche Semaphor 103972889.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5409
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:47.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:36.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4167
p-value of test                       :    0.9951


-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:02.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:01.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:51.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:59.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.36
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:13.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:43.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.01
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.03
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.56
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.22
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.43
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.77
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:59.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7176.12
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.58
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.22
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:01.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.47
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.46
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:35.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5095.39
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:06.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45914
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869914
  j =  1                              :        399908178
  j =  2                              :            45902
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45620
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869620
  j =  1                              :        399908762
  j =  2                              :            45616
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9946


-----------------------------------------------
CPU time used                    :  00:02:27.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:16.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:33.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.84e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.88e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 2.30e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.07
p-value of test                       :  8.1e-3

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.22
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:48.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.34
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.03
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.10
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.68
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.42
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.59
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.96
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.74e-3
p-value of test                       :    0.9928

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   95.30
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17726.95
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:52.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.45
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.82
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.44
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.11
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.26
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.53
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.03
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.52
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.26
p-value of test                       :    0.9969


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.52
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.02
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.62
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.71
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.96
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.45
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.85
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.80
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  170.59
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.00
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.70
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.10
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.81
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.72
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.49
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.90
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.11
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.96
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.33
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.69
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.49
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:24.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.00
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:25.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.40e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.19e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 7.52e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.97
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.08
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.83
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:08.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.38
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:08.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.94
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9752.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:39.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.37
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.66
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:56.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.20
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11981.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11721.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.82
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999836630

Normal statistic for number of bits   :   -1.29
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.50
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000050251

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.050
p-value of test                       :    0.52

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9906

Tests on the sum of all N observations
Standardized normal statistic         :   0.058
p-value of test                       :    0.48

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:00.85

 All tests were passed




Server wird beendet - Lösche Semaphor 105152537.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:51.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:48.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:38.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:36.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4460
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:05.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:02.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:52.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:59.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    2.76
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    3.26
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     335
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:11.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    3.10
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     178
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:40.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   46.81
p-value of test                       :  2.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.61
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.25
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.10
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:48.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1475.20
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:07.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6947.20
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.50
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.40
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:09.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.85
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.05
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:36.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5168.69
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:56.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45829
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869829
  j =  1                              :        399908347
  j =  2                              :            45819
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45815
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869815
  j =  1                              :        399908376
  j =  2                              :            45803
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:28.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:18.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:03.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.50e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.63e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.42e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.026
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:39.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.98
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.92
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.88
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.90
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.28
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.88
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17577.11
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:52.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.77
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.67
p-value of test                       :    0.9912


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.69
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.82
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.23
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.79
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.50
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.25
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.68
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.76
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  414.35
p-value of test                       :    0.9979


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.61
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.01
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.76
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.04
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.55
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.06
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.30
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.48
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.75
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5207.95
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.82
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.26
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.45
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.86
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.73
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.09
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.04
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.72
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:22.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.84
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:25.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.88e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 8.20e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 2.62e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.42
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.67
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.26
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:06.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10019.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9875.12
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:04:22.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:53.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.01
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:55.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4197.83
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.08
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:31.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12036.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:31.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.97
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999839681

Normal statistic for number of bits   :   -1.27
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.13
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999810770

Normal statistic for number of bits   :   -1.50
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:14.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 28  SimpPoker, r = 0                2.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 106037273.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:52.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5472
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:52.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:55.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:00.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:01.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:54.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:00.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:50.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:18.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:45.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.92
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.79
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.67
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.41
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.75
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:43.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1529.54
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7234.13
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:42.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.82
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.09
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:02.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.23
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.62
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4981.98
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:55.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46117
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870117
  j =  1                              :        399907768
  j =  2                              :            46113
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46187
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870187
  j =  1                              :        399907629
  j =  2                              :            46181
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:27.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:19.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:02.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:53.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 3.95e-4
p-value of test                       :  1.9e-3

Anderson-Darling statistic = A2       :    4.90
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.51e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:34.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.88
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.87
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.67
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.52
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.11
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.92
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.76
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.67
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17431.33
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.15
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.89
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.67
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.10
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.83
p-value of test                       :  6.5e-3


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.36
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.71
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.53
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.73
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.84
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.57
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.43
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.90
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.22
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.38
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.60
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.17
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.29
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.03
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.46
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.35
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.01
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.81
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.37
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.74
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.48
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.65
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.13
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.73
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.53
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    1.83
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:25.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.19
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:24.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 7.86e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.59
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.62
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.27
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:07.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:06.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10235.82
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10102.08
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:48.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4801.23
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:49.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5121.76
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:50.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4247.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11732.35
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11748.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.67
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999876206

Normal statistic for number of bits   :   -0.98
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   30.89
p-value of test                       :    0.9952


-----------------------------------------------
Total number of bits:  7999903440

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    4.32
p-value of test                       :  6.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.79
p-value of test                       :    0.9974

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:45.96

 All tests were passed




Server wird beendet - Lösche Semaphor 107216921.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:53.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:59.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:06.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7471
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:09.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:11.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7460
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:12.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:12.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.50
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.28
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.16
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.92
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.59
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.40
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.95
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:26.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7073.27
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:07.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.26
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:16.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.04
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.43
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:40.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5046.45
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:00.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45925
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869925
  j =  1                              :        399908151
  j =  2                              :            45923
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46136
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870136
  j =  1                              :        399907729
  j =  2                              :            46134
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:33.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:24.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:13.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:01.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.27e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:24.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 9.60e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:24.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:51.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.66
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.38
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:03.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.46
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.93
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.20
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17531.59
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.13
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.98
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.14
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.25
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.83
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.89
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.05
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.50
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.88
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.29
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.98
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.75
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.27
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.04
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.53
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.43
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.79
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  588.10
p-value of test                       :  3.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.98
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.66
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.54
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.70
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.42
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  322.94
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.65
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.76
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.63
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.27
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.10
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.60
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.76
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.64
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -1.58
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.30e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.78
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.48
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.83
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:09.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.78
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:09.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10217.75
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.46
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.064
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:04:30.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5016.47
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5074.21
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:00.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11853.41
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11577.72
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:36.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.64
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000126229

Normal statistic for number of bits   :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.76
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999884336

Normal statistic for number of bits   :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    2.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:51.47

 All tests were passed




Server wird beendet - Lösche Semaphor 108101657.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:51.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7484
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:03.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:04.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:54.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:00.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:13.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:39.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.15
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.77
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   85.10
p-value of test                       :  4.4e-3

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.90
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.71
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  173.95
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.00
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1382.77
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7250.57
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.37
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.10
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:02.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.96
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  153.39
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:32.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5028.43
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:11.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45876
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869876
  j =  1                              :        399908251
  j =  2                              :            45870
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46024
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870024
  j =  1                              :        399907956
  j =  2                              :            46016
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:26.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:16.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:54.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.11e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.20
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.75
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:48.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.50
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   67.22
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:36.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.04
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.34
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17506.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.87
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.43
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.28
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.42
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.77
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.88
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.86
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.67
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.97
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.86
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.41
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.51
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.47
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.58
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.58
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.41
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.54
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.09
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.61
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.26
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.00
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.02
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.47
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.48
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.25
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.03
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.55
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.10
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.49
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.12
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.95
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.75
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:23.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.97e-3
p-value of test                       :    0.9948

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.12
p-value of test                       :  8.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.85
p-value of test                       :  2.2e-3

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.91e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 9.71e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.94e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.08
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   22.11
p-value of test                       :  4.7e-3

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.92
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.51
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9799.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10230.81
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:41.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.14
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.32
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.70
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.90
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11736.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.24
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.41
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999958715

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.60
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000066319

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.15
p-value of test                       :    0.02

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:48.09

 All tests were passed




Server wird beendet - Lösche Semaphor 109412377.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:52.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1267
p-value of test                       :    0.9959

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334387
  j =  1                              :        599997466
  j =  2                              :             1267
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:42.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:59.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:01.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:10.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:11.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:09.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:13.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.17
p-value of test                       :    0.9965

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    2.09
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:13.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:44.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.24
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.86
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.91
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.85
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.11
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.54
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.71
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:58.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6854.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.34
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:12.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.64
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.44
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4899.25
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45550
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869550
  j =  1                              :        399908904
  j =  2                              :            45542
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45778
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869778
  j =  1                              :        399908445
  j =  2                              :            45776
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:30.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:21.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:09.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:57.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.032
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:24.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   98.84
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.29
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.85
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.11
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.58
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.20
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.54
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.97
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17221.82
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.33
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.67
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.58
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.09
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:39.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.13
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.24
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.32
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.42
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.51
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.81
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.20
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.82
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.28
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.80
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.52
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.08
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.97
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.04
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.95
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  470.55
p-value of test                       :  1.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.47
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.13
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.88
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.52
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.53
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.34
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.33
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.40
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.56
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   0.061
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:24.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.79
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :  -0.060
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:24.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.21e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.74
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.87
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:04.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.17
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:07.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10103.85
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10174.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:11.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:04:35.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.88
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:53.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5028.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4231.21
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.40
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.28
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11761.79
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.02
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000164710

Normal statistic for number of bits   :    1.30
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.71
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999985157

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.18
p-value of test                       :  7.5e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.84
p-value of test                       :  2.3e-3

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:57.70

 All tests were passed




Server wird beendet - Lösche Semaphor 110329881.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5512
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:53.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:05.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:05.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:58.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:00.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.22
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:14.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.41
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:42.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.34
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.14
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.84
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.28
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.45
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  474.87
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1475.35
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:03.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6813.33
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.32
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:06.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.24
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:46.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.70
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.13
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:00.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45847
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869847
  j =  1                              :        399908309
  j =  2                              :            45841
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45793
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869793
  j =  1                              :        399908417
  j =  2                              :            45787
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:29.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:44.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:35.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 5.23e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.43e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.83e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:28.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.020
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:41.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.96
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.66
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.39
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:45.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.39
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.69
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.23
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.4e-3

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.68
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.6e-3

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17780.65
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.22
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.87
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.15
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.22
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.93
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.83
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.09
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.57
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.12
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.96
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.59
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.80
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.14
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.77
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.73
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.28
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.99
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.52
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.86
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.38
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.22
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4878.47
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.79
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.34
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.43
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  298.82
p-value of test                       :    0.9995    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.73
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.58
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.76
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.89
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    2.05
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:24.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.43
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.61e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.47e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.96
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.84
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.13
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:06.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.08
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:05.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10095.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:57.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.41
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4980.06
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.21
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4046.92
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11987.58
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.82
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000125662

Normal statistic for number of bits   :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.21
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999975029

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.13
p-value of test                       :    0.9990    *****

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:57.55
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 M (L=10000, r=15)   0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 111509529.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997287
  j =  2                              :             1355
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5331
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:53.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4207
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:05.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:05.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:55.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:01.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.91
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    3.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.20
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:13.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.16
p-value of test                       :    0.9980


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.88
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:41.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.77
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.79
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.01
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  195.57
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.69
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7077.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.97
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:03.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.98
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.32
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:33.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4972.00
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:03.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45513
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869513
  j =  1                              :        399908977
  j =  2                              :            45507
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46065
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870065
  j =  1                              :        399907874
  j =  2                              :            46057
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:27.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:19.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:35.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 8.54e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 6.09e-6
p-value of test                       :    0.9985

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.064
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.33
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.04
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.91
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.80
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.62
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:43.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.83
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.56
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17295.39
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.14
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.48
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.29
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.42
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.96
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.13
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.23
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.35
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.93
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.28
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.54
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.86
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.59
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.33
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.22
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.19
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.19
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.10
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.04
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.75
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4831.33
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  455.47
p-value of test                       :  3.8e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.16
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.62
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.66
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.76
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.16
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.86
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.19
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.59
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:21.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.63e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.54e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 9.11e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.24
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.26
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.74
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:05.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.03
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 2.59e-3
p-value of test                       :    0.9974

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9824.30
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9761.05
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:36.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.66
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.93
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.58
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11840.02
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12076.40
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.99
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000036625

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.49
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000099637

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.84
p-value of test                       :    0.97

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   0.021
p-value of test                       :    0.49

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:06.50

 All tests were passed




Server wird beendet - Lösche Semaphor 112525337.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:40.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:51.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:05.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:06.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:56.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:02.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.85
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:13.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:43.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.89
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.60
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.79
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.70
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.31
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.92
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:42.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1531.12
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6989.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.70
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.28
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:03.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.10
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.85
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:32.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5095.32
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:01.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45734
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869734
  j =  1                              :        399908535
  j =  2                              :            45728
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45926
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869926
  j =  1                              :        399908155
  j =  2                              :            45912
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:27.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:18.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-3
p-value of test                       :    0.9989

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :  3.3e-3

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  5.6e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:55.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 8.78e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.65e-6
p-value of test                       :    0.9977

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:38.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.65
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.34
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.51
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.03
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:47.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.29
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 9.91e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.00
p-value of test                       :  9.1e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   19.90
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.93
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9985

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17409.58
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:52.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.93
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.94
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.52
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.36
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.51
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   64.24
p-value of test                       :  1.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.02
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.77
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.94
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.99
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.27
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.10
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.33
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.07
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.91
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.80
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.54
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.99
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.69
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.45
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4893.09
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.25
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.01
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.09
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.90
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.53
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.07
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.86
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.01
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -1.49e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:20.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.25
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.42e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.49e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.66
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.46
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-3
p-value of test                       :    0.9977

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  2.8e-3

Anderson-Darling statistic = A2       :    4.04
p-value of test                       :  8.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  261.08
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:02:06.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.19
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.83
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9937.99
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:38.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.14
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.05
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.09
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.09
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11946.03
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12213.37
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.19
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000085963

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.54
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000167116

Normal statistic for number of bits   :    1.32
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.93
p-value of test                       :    0.03

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    2.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :  -0.031
p-value of test                       :    0.51

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:05.79

 All tests were passed




Server wird beendet - Lösche Semaphor 113541145.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:13.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5515
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:51.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:39.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:05.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:05.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:55.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:01.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    2.00
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.32
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    3.93
p-value of test                       :  9.5e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     256
p-value of test                       :    0.9949

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:14.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.62
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.59
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.56
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.39
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:44.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.30
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:59.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7094.22
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:44.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.49
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.51
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:03.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.88
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.11
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:34.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5230.24
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:02.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45737
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869737
  j =  1                              :        399908528
  j =  2                              :            45733
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46464
p-value of test                       :  3.2e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870464
  j =  1                              :        399907073
  j =  2                              :            46462
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:27.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:18.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:45.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.94e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.78e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:39.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:39.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.10
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.54
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.86
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.66
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.31
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.87
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17121.11
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.82
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.18
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.72
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.57
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.04
p-value of test                       :    0.9929


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.34
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.95
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.62
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.50
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.09
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.15
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  562.76
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.52
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.53
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.52
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.84
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.49
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.46
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.84
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.22
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.15
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5164.48
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.66
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.28
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.32
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.34
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.93
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.22
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.93
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :   0.066
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:22.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.18
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    1.39
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:23.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9945

Tests on the sum of all N observations
Standardized normal statistic         :   0.098
p-value of test                       :    0.46

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.63e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.22e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 5.57e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.26
p-value of test                       :    0.9960

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.87
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.19
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:05.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.58
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.59
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10060.77
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:37.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5059.45
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:50.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11966.16
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11639.29
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.58
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999954980

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.54
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000040018

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:23.23

 All tests were passed




Server wird beendet - Lösche Semaphor 114524185.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5351
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:50.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4239
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:39.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4242
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:56.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:05.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:04.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:54.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:00.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    3.53
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    4.58
p-value of test                       :  4.6e-3

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:11.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.10
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    2.27
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:39.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   20.05
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.12
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.34
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.96
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.89
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.51
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.65
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:01.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6997.09
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.80e-3
p-value of test                       :    0.9930

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.78
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:05.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.03
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.31
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5108.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:03.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46354
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870354
  j =  1                              :        399907296
  j =  2                              :            46346
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45830
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869830
  j =  1                              :        399908344
  j =  2                              :            45822
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:27.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:19.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:44.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:33.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 9.71e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.014
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:37.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.29
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.65
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.49
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.51
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.43
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.46
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.94
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.89
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.41
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17285.98
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.31
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.81
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.26
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.03
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.51
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.43
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.61
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.70
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.91
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.68
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.03
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.12
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.41
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.47
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.16
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.31
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.86
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.28
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.33
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.72
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.21
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.71
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.20
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.13
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  321.23
p-value of test                       :    0.9913


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  450.20
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.98
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.68
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.23
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.63
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:22.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.88
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:22.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.82
p-value of test                       :    0.97

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.05e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.91e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.20
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.73
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  160.87
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:05.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.16
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:06.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9953.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10305.83
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:40.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.98
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.03
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4015.42
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11626.56
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11950.31
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.69
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999986066

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.16
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000008089

Normal statistic for number of bits   :   0.064
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.42
p-value of test                       :    0.9921

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:03.70

 All tests were passed




Server wird beendet - Lösche Semaphor 115441689.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5413
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:55.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7170
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:04.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:01.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:12.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:40.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.67
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.53
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    5.37
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.48
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.08
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.23
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.15
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.19
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1492.51
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6962.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:40.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.89
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:03.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.05
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.69
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5162.11
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:58.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45688
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869688
  j =  1                              :        399908626
  j =  2                              :            45684
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45851
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869851
  j =  1                              :        399908302
  j =  2                              :            45843
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:27.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 7.49e-4
p-value of test                       :    0.9992    *****

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9941


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:18.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:45.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9972


-----------------------------------------------
CPU time used                    :  00:01:58.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:33.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.65e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.44
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:37.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.84
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.37
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.21
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.88
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.97
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.36
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:39.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.22
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9953

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.57
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.054
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   11.89
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17241.94
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.53
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.61
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.51
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.15
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.40
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.36
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.48
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.68
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.48
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.25
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.92
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.42
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.35
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.79
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.78
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.57
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.12
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.54
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.53
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.15
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4889.59
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.79
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.45
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.80
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.51
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.04
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.53
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.06
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.14
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:22.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.34
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.12e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.20e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.22
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.10
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.17
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:03.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.98
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:04.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10108.38
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.32
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:42.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.42
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:51.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4261.73
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.82
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11969.63
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11712.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.74
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000012070

Normal statistic for number of bits   :   0.095
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.24
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000083536

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.24

Sample variance                       :    2.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:41.22

 All tests were passed




Server wird beendet - Lösche Semaphor 116391961.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5484
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:54.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:04.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:04.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:55.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:00.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:14.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.41
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.97
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.66
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.21
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.72
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.13
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7107.45
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:41.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.73
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   38.55
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:02.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.05
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.37
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:33.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5113.18
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:59.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45504
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869504
  j =  1                              :        399908993
  j =  2                              :            45502
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45787
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869787
  j =  1                              :        399908427
  j =  2                              :            45785
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:27.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9925

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:18.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 8.44e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.19e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.50e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.43
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:36.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.28
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.31
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.37
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.71
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   13.23
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17413.42
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.64
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.08
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.73
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.38
p-value of test                       :    0.9967


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.09
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.34
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.17
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.66
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.23
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.89
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.04
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.42
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.03
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.41
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.64
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.98
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.76
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.27
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.23
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.00
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.70
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.45
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4922.47
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.26
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.03
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.51
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.31
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4900.16
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.90
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.87
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.39
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:26.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.25
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:25.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.65e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.20
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.61
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:04.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.3e-3

Anderson-Darling statistic = A2       :    4.66
p-value of test                       :  4.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  248.55
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10239.18
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9974.13
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.29
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:41.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.85
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4706.54
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:50.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3976.26
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4160.89
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11860.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11483.02
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.35
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999911219

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.98
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000118822

Normal statistic for number of bits   :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.66

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:53.57

 All tests were passed




Server wird beendet - Lösche Semaphor 117407769.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:51.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5611
p-value of test                       :  5.2e-3


-----------------------------------------------
CPU time used                    :  00:03:55.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:57.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:05.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:56.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:01.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    2.69
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    2.97
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     532
p-value of test                       :    0.9975

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.83
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:15.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:42.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.71
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.44
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.87
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.27
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.07
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.57
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7013.93
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:41.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.13
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    4.41
p-value of test                       :  5.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.86
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:02.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.48
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.37
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5223.82
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:03.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45952
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869952
  j =  1                              :        399908099
  j =  2                              :            45946
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45695
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869695
  j =  1                              :        399908615
  j =  2                              :            45685
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:28.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:18.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:59.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:55.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.67e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 8.08e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:35.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.03
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.87
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.16
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.56
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.40
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.62
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.88
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.61
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17148.36
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.71
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.70
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.19
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.40
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.16
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.67
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.92
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.06
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.35
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.56
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.52
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  190.24
p-value of test                       :  8.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  437.46
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.41
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.32
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.78
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.62
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  584.34
p-value of test                       :  5.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.87
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.90
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.21
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.73
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5185.82
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.05
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.43
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.30
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.89
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.06
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  452.22
p-value of test                       :  5.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.02
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.94
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :  -0.015
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:23.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.35
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    1.24
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 4.93e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.57e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.00
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.60
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.72
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:02.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:04.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.81
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9922.42
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.21
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:50.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3981.36
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4209.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11963.32
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11466.77
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.66
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000078502

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.69
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000020020

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9955

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.43

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.09
p-value of test                       :    0.98

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:15.95

 All tests were passed




Server wird beendet - Lösche Semaphor 118358041.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5441
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:56.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7555
p-value of test                       :  3.0e-3


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:57.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:04.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:04.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:55.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:01.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.15
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     551
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:14.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    4.24
p-value of test                       :  6.6e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     122
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:44.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.81
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.65
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.26
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.44
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  195.63
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.37
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:44.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.03
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7099.93
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:42.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.65
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.22
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:03.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.63
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.73
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:33.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5186.75
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:00.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46395
p-value of test                       :  8.2e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870395
  j =  1                              :        399907213
  j =  2                              :            46389
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45496
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869496
  j =  1                              :        399909011
  j =  2                              :            45490
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:26.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:18.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  8.3e-3

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:55.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:32.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.72e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 8.13e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.97e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.97
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.61
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.59
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.93
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.14
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.54
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.70
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.07
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.14
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17591.66
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.30
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.21
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.73
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.54
p-value of test                       :    0.9929


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.90
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   47.18
p-value of test                       :  4.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.82
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.20
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.09
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.86
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.84
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.08
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.45
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.79
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.41
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.19
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.44
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.96
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.99
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.41
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.74
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.34
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.72
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.98
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4938.62
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.82
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.03
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.26
p-value of test                       :    0.9934


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:22.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.51
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:22.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 4.71e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.82
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.35
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.09
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:03.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.89
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:04.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10089.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9837.89
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:41.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4771.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.10
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.78
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.64
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11993.27
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.77
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.88
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000030952

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.65
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999978938

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:58.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 51  SampleProd, t = 16              0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 119341081.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:39.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:51.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5406
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:56.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7167
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:41.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:04.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:54.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:01.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:14.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.73
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:43.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.80
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.45
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.25
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.59
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.06
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  194.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.40
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.13
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:00.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6817.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 3.21e-4
p-value of test                       :    0.9997    *****

Anderson-Darling statistic = A2       :    5.07
p-value of test                       :  3.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.43
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.21
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:02.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.16
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.22
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5070.44
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:03.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45665
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869665
  j =  1                              :        399908674
  j =  2                              :            45657
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45990
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869990
  j =  1                              :        399908021
  j =  2                              :            45988
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  1.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    3.86
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:26.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:19.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:46.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:00.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 6.23e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.49e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.047
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:38.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:36.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.89
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.20
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.18
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.58
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.64
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.60
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.20
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.85
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17163.28
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.75
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.39
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.59
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.72
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.40
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.76
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.54
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.95
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.70
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.53
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.62
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.50
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.52
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   95.90
p-value of test                       :    0.9963


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.09
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:51.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.19
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.35
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.99
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.69
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.72
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:51.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.67
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.14
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5136.84
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  296.79
p-value of test                       :    0.9992    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.56
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.40
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.49
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5126.00
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.29
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.07
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.20
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.44
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 8.56e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.00
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.45
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.04
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:03.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.59
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:04.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9896.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.050
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:39.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.85
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:50.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.36
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11786.40
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11614.97
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.48
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000048580

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.71
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999962894

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:37.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 R (L=10000, r=0)    0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 120356889.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:56.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:05.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:05.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:56.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:01.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.57
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:15.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:41.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.62
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.74
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.54
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.15
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.32
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:45.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1572.38
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7044.60
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.35
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.51
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:03.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.92
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:46.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  149.53
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5150.64
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:16.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45707
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869707
  j =  1                              :        399908589
  j =  2                              :            45701
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45977
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869977
  j =  1                              :        399908053
  j =  2                              :            45963
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:27.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:19.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:02.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:37.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.66
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   38.16
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.49
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.74
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.17
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.63
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:41.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9958

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.15
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.70
p-value of test                       :  4.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16894.53
p-value of test                       :    0.9981



-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.43
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.25
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.47
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.94
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.16
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.05
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.76
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.63
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.32
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.25
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.58
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.90
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.83
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.65
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.22
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.04
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.64
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.14
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.06
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.98
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5081.80
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.33
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.49
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.06
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.18
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.58
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.45
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:34.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.96
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:21.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.95
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:20.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.54e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 3.57e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.73
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.50
p-value of test                       :    0.9927

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:02.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10124.17
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10165.90
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.074
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:51.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:25.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.88
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.04
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.94
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11830.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11518.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.85
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000003712

Normal statistic for number of bits   :   0.029
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.94
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000152797

Normal statistic for number of bits   :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  6.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.85
p-value of test                       :    0.97

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:00:09.56

 All tests were passed




Server wird beendet - Lösche Semaphor 121405465.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5399
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:45.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:38.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:38.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7130
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:08.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:08.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:07.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:11.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.76
p-value of test                       :  3.8e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    5.22
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.25
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.76
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:13.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:44.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.68
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.99
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.17
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.10
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.13
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.04
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1387.60
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:09.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6956.27
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:54.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.63
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.69
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:18.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.26
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:47.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.23
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5079.97
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:59.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45825
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869825
  j =  1                              :        399908356
  j =  2                              :            45813
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45653
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869653
  j =  1                              :        399908698
  j =  2                              :            45645
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:27.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:17.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:52.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:09.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.16e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.87e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.34e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:24.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.40
p-value of test                       :  8.1e-3

-----------------------------------------------
CPU time used                    :  00:01:53.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:53.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.71
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.73
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.47
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:53.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.04
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.94e-3
p-value of test                       :    0.9948

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.74
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   13.52
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17261.19
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.57
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.11
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.21
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.07
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.15
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.19
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.85
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.38
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.24
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.50
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.92
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.65
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.26
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.21
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.37
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.19
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.64
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.54
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.74
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.32
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.51
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.47
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.98
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.83
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.94
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.35
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.47
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.46
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -1.41
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:27.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.87
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -1.49e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:25.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :  8.3e-3

Kolmogorov-Smirnov- statistic = D-    : 7.97e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.67e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.75
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.35
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:31.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:16.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:16.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10147.78
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10213.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:04:41.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:53.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4769.54
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:55.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.09
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.61
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11941.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:32.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12009.97
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:34.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.26
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999906107

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.71
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999925757

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.81

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:20:11.52

 All tests were passed




Server wird beendet - Lösche Semaphor 102432794.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:50.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:10.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:12.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:09.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:13.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:13.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:42.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.29
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.36
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.49
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.81
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.73
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.17
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  375.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:57.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:02.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7039.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.46
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.08
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.89
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5109.77
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:54.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45694
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869694
  j =  1                              :        399908618
  j =  2                              :            45682
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46215
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870215
  j =  1                              :        399907571
  j =  2                              :            46213
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:29.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:16.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:04.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:38.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 5.72e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.67e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:24.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:50.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.68
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.74
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.56
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:51.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.28
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.92
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.09
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.08
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17435.66
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.08
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.86
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.12
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.50
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.77
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.11
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.58
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.33
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.95
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.07
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.88
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.31
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.19
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.03
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.59
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  582.63
p-value of test                       :  6.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.06
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.58
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.80
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.80
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.10
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  150.37
p-value of test                       :    0.9964


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.46
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.94
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.40
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.71
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.41
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.77
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.75
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:23.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.83e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.66e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.42
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.34
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:08.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.51
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:07.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10156.51
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9885.33
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:04:19.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5027.60
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.88
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:50.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.91
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3926.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11952.02
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11720.43
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:31.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.98
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999862994

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.15
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999863123

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:47.17

 All tests were passed




Server wird beendet - Lösche Semaphor 103546906.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:48.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:27.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5413
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:53.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:05.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:06.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:56.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:03.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    2.27
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9954

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.17
p-value of test                       :    0.9960

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:10.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:35.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.36
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.50
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.58
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.89
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.04
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.06
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.70
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.00
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1409.29
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6971.71
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.97
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.13
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:06.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.82
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.51
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:32.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4836.11
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:51.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45889
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869889
  j =  1                              :        399908225
  j =  2                              :            45883
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46079
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870079
  j =  1                              :        399907846
  j =  2                              :            46071
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:26.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:16.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:45.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:00.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:37.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.34e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.37e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:40.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.67
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.54
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.85
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.99
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.61
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   50.35
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.04
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.72
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.32
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17410.85
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.57
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.08
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.98
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.87
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.37
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.31
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.61
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.41
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.09
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.38
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.10
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.71
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.79
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.91
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.38
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.14
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.41
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.38
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.18
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.50
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  308.77
p-value of test                       :    0.9962


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.38
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.31
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.21
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.81
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.66
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.91
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.46
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:23.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.25
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.80e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 6.73e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 5.70e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.64
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.87
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.01
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:08.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.73
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:06.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.75
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10257.11
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.051
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:38.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.17
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3996.43
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4276.11
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11941.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11714.58
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.96
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000032047

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.96
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999895490

Normal statistic for number of bits   :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :  -0.090
p-value of test                       :    0.54

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:00:57.45

 All tests were passed




Server wird beendet - Lösche Semaphor 104595482.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5347
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:49.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4159
p-value of test                       :    0.9966


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:07.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:06.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:57.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:46.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    2.54
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    3.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:14.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.62
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    2.80
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     187
p-value of test                       :  2.0e-3

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.12
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.95
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.56
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.44
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  279.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.77
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.34
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7122.17
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.22
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:06.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.85
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.78
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:35.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4883.72
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:52.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908070
  j =  2                              :            45959
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45625
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869625
  j =  1                              :        399908754
  j =  2                              :            45617
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:26.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:18.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:00.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 7.87e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.99e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.74e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:40.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -4.55e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.67
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.62
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.38
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:44.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.46
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17251.46
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.55
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.51
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.24
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.36
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.44
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.17
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.88
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.26
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.44
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.06
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.86
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.89
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.68
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.31
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.30
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.67
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.79
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.66
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.88
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.45
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5111.43
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  435.83
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.14
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.94
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.01
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4884.60
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.67
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.79
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.96
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:24.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.74
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:25.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.09e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.44e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.84
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.04
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:07.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    4.19
p-value of test                       :  7.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.38
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:07.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9694.93
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9956.04
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.026
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:55.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:49.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5048.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4307.86
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.23
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11765.50
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.17
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   88.91
p-value of test                       :  1.9e-3


-----------------------------------------------
Total number of bits:  7999903269

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.66
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999975974

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:28.04

 All tests were passed




Server wird beendet - Lösche Semaphor 105578522.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5519
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:53.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7469
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:11.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:11.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:07.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     639
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.86
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:14.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:42.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.27
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.30
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.63
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.22
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.41
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.68
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:54.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1497.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:05.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7162.28
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   49.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.16
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:16.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.62
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.01
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4937.81
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:55.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908185
  j =  2                              :            45903
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908203
  j =  2                              :            45891
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:30.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:19.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  3.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:06.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.43e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:24.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:45.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.68
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.03
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.68
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.15
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.56
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.16
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9922

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.28
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17445.87
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.23
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.87
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.03
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.05
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.04
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.10
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.78
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.07
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.59
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.33
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.88
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.59
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.23
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.63
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.04
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.00
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.70
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.90
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5103.55
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.54
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.25
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.36
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.76
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.44
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  429.73
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.99
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.25
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.11
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.08e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.42
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.45
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.49
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.37
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:05.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9816.61
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9809.40
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:04:18.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9906

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.10
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:53.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:54.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.81
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4021.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11753.51
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11679.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.66
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000112093

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   82.37
p-value of test                       :  7.7e-3


-----------------------------------------------
Total number of bits:  8000114058

Normal statistic for number of bits   :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:12.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:12.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:46.82

 All tests were passed




Server wird beendet - Lösche Semaphor 106561562.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:48.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5480
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:56.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4218
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:44.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:11.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:13.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:11.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:16.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    2.11
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:49.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     641
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:15.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:47.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.78
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.09
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.92
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.85
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.99
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.60
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:58.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.40
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:08.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6947.80
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.27
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.71
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:22.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.90
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.02
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:44.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5016.81
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:54.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45645
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869645
  j =  1                              :        399908713
  j =  2                              :            45639
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45874
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869874
  j =  1                              :        399908263
  j =  2                              :            45852
  j =  3                              :               11
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:31.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9956


-----------------------------------------------
CPU time used                    :  00:02:20.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:08.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 8.70e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.99e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:44.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.31
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   96.64
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.56
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.44
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.96
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:51.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.73
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.43
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.34
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 4.86e-4
p-value of test                       :    0.9995    *****

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17929.34
p-value of test                       :  4.0e-3



-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.40
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.42
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.00
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.00
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.78
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.67
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.11
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.51
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.67
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.51
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.54
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.51
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.14
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.92
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.43
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.31
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.73
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.87
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.63
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.04
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.36
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.06
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.27
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.80
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.86
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.73
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.45
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.32
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.73
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.31
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :    2.31
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:02:24.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.40
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:24.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.97
p-value of test                       :    0.98

Sample variance                       :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.09e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 7.29e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.12e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.01
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.99
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.41
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:02.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.87
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:02.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10038.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9916.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    3.12
p-value of test                       :  9.1e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:04:21.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4737.91
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.81
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:59.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4236.78
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11740.48
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:34.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11838.01
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:35.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.60
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999886916

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.26
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999922235

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.090
p-value of test                       :    0.46

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:08.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 92  HammingCorr, L = 30             9.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 107610138.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:48.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5478
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:55.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4229
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:58.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:06.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:05.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:55.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:59.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.29
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    2.37
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:15.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.37
p-value of test                       :  6.4e-3

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:42.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.23
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.83
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.71
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.87
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.46
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.89
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.78
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.79
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.36
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7049.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.20
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.06
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:03.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.00
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.55
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5148.06
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:11.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:59.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45857
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869857
  j =  1                              :        399908288
  j =  2                              :            45853
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45813
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869813
  j =  1                              :        399908377
  j =  2                              :            45807
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:28.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:18.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:00.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.61e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:36.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.93
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.63
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:37.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.61
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.14
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.48
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17400.90
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.12
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.17
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.80
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.87
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.22
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.66
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.04
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.08
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.71
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.09
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.08
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.18
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.32
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.97
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.78
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.71
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.45
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.90
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.02
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.99
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.53
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.22
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  285.02
p-value of test                       :    0.9999    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.09
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.45
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.10
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5159.27
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.13
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.86
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.23
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   0.079
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:22.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.93
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:25.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.21
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.90e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.77e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 5.09e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.84
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.76
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.92
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:04.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.41
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:03.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10120.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.42
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.100
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:31.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4957.87
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4980.71
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.10
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4028.63
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11753.67
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11863.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.24
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000187174

Normal statistic for number of bits   :    1.48
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.98
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000008470

Normal statistic for number of bits   :   0.067
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:00.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 R (L=10000, r=0)    0.9999 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 108658714.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1462
p-value of test                       :  4.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334582
  j =  1                              :        599997076
  j =  2                              :             1462
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5437
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:55.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:59.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:08.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7169
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:08.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:03.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:06.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.79
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:16.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:44.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.77
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.59
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.24
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.74
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1382.79
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:07.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7153.82
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.03
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.88
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:09.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.99
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.08
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5148.71
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:54.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46009
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870009
  j =  1                              :        399907984
  j =  2                              :            46005
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45716
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869716
  j =  1                              :        399908573
  j =  2                              :            45706
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:30.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:18.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:07.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:57.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.5e-3

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.74e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.05e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.19
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.90
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.89
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.38
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.09
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.98
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.60
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.37
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17521.88
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.30
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.34
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.73
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.74
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.11
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.05
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.84
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.89
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.96
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.12
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.84
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.43
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.15
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.23
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.76
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.63
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.64
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.83
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.30
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.86
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.64
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4819.28
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.24
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.53
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.50
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.81
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.35
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.79
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.14
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -1.78
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:22.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.47
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -1.72
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:22.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.85e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.59
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.89
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.51
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:02.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.17
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :  8.5e-4    *****

Anderson-Darling statistic = A2       :    4.60
p-value of test                       :  4.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10358.99
p-value of test                       :  6.0e-3

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:04:03.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:51.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:51.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.02
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3932.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:29.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11760.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.50
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999884717

Normal statistic for number of bits   :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.72
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999986240

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:39.02

 All tests were passed




Server wird beendet - Lösche Semaphor 109641754.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1265
p-value of test                       :    0.9966

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334385
  j =  1                              :        599997470
  j =  2                              :             1265
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5515
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:55.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7151
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:06.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:55.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7150
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:01.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    2.36
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     947
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:17.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:46.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.29
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.38
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.99
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.13
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.60
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.79
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  480.92
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:44.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1504.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6889.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.14
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.75
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:06.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.45
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.71
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:33.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5294.44
p-value of test                       :  6.0e-3


-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:59.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45992
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869992
  j =  1                              :        399908020
  j =  2                              :            45984
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45889
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869889
  j =  1                              :        399908226
  j =  2                              :            45881
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:28.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:59.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.82e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:37.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:38.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.33
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.42
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.67
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.99
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.15
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.70
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.56
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17389.08
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.05
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.37
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.08
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.53
p-value of test                       :    0.9962


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.73
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.86
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.50
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.36
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.34
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.43
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.20
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.48
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.61
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.89
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.11
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.32
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.32
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.73
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.11
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.61
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.24
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.06
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.48
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.03
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5167.93
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.59
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.47
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.81
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :   -1.20
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:21.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   34.64
p-value of test                       :  5.3e-4    *****


-----------------------------------------------
Normal statistic for number of jumps  :  -0.086
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:21.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.95
p-value of test                       :  9.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.72
p-value of test                       :    0.9968

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.90
p-value of test                       :    0.97

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 6.90e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.05
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.72
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.37
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:03.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.93
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:02.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9945.31
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:33.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4662.07
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4015.76
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.01
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11764.72
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11803.01
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.70
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999826214

Normal statistic for number of bits   :   -1.37
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.78
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000025693

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:30.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 81  LinearComp, r = 0               5.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 110690330.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:55.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7484
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:05.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:05.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:55.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:00.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:16.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:44.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.87
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.72
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.97
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.24
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.12
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.44
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.34
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  276.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.02
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1261.89
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6828.20
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.88
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.94
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:04.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4814.27
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:03.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46006
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870006
  j =  1                              :        399907992
  j =  2                              :            45998
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46122
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870122
  j =  1                              :        399907757
  j =  2                              :            46120
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:28.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  6.6e-3

Anderson-Darling statistic = A2       :    4.14
p-value of test                       :  7.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  4.6e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:58.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :  2.2e-3

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:33.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.91e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.89e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:44.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.025
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.57
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.91
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.63
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.88
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.68
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.15e-3
p-value of test                       :    0.9946

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.20
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.03
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.60
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17109.16
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.41
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.03
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.58
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.44
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.82
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.54
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.07
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.19
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.65
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.67
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.25
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.12
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.51
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.16
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.36
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.47
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.65
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.35
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.98
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.34
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.35
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.01
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.59
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.51
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  486.52
p-value of test                       :  2.9e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.75
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.79
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.90
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.59
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :  -0.086
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:25.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.18
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :   -1.26
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:23.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    2.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.95e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.78
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.40
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:03.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.66
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:03.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10149.97
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.54
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:36.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5043.20
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4767.92
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.62
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.65
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11793.76
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.07
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.71
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999972062

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.85
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999823472

Normal statistic for number of bits   :   -1.40
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    3.85
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    3.07
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:24.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 36  Gap, r = 0                      0.9997 
 79  RandomWalk1 M (L=10000, r=15)   2.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 111706138.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5406
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:54.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:41.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:57.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:07.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:07.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:02.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:06.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    2.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:16.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.64
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.59
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.58
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.07
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  192.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.30
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:03.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7094.62
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.92
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:08.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.01
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.00
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:36.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5015.38
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:01.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45946
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869946
  j =  1                              :        399908111
  j =  2                              :            45940
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45598
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869598
  j =  1                              :        399908804
  j =  2                              :            45598
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:30.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:18.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:56.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.33e-3
p-value of test                       :    0.9903

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:36.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 9.71e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.99e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.030
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:44.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:44.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.03
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.79
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.59
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.26
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.05
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.70
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17449.02
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.96
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.80
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.18
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.12
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.00
p-value of test                       :    0.9929


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.12
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.47
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.03
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.87
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.34
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.43
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.95
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.24
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.05
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.98
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.40
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.12
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.69
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.84
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4865.89
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.76
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.31
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.24
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.82
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.06
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.00
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.99
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -2.41
p-value of test                       :    0.9920



-----------------------------------------------
CPU time used                    :  00:02:20.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.70
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:21.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.84e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.78
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.31
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.85
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:04.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.96
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:03.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9842.05
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.10
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:04:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.41
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:51.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.54
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:51.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.82
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.57
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11977.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11719.19
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.17
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999961193

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.69
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999833114

Normal statistic for number of bits   :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.80
p-value of test                       :    0.04

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:33.29

 All tests were passed




Server wird beendet - Lösche Semaphor 112656410.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:48.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:56.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:05.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:06.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:57.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:02.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     651
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:15.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:45.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.98
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.29
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.39
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.51
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.40
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.12
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.21
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.25
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:45.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1400.59
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6996.32
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.32
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.38
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:04.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.45
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.95
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:32.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5185.73
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:58.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45761
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869761
  j =  1                              :        399908483
  j =  2                              :            45751
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45903
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869903
  j =  1                              :        399908197
  j =  2                              :            45897
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:29.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:18.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:54.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:34.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.24e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:35.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.39
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.60
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.27
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.52
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   11.29
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:01:39.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.74
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.62
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.88
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.64
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.53e-3
p-value of test                       :    0.9908

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  163.59
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17692.22
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.54
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.13
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.64
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.98
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.56
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.24
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.59
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.51
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.97
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.92
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.56
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.94
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.24
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.27
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.37
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.93
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.64
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.45
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.07
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.98
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.23
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  312.65
p-value of test                       :    0.9939


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  245.35
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.22
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.17
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5090.45
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.47
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.51
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.55
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -0.82
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.45
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:22.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.15
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.99e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 8.52e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.54e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.57
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.22
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :  8.9e-4    *****

Anderson-Darling statistic = A2       :    7.23
p-value of test                       :  2.9e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  273.73
p-value of test                       :  4.1e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:03.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.29
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:03.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10137.21
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.26
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:37.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4814.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:48.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4282.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11942.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11929.88
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.69
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000076801

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.81
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999945986

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.96

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:53.02
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 88  PeriodsInStrings, r = 0         4.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 113704986.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:48.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5520
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:56.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4456
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:06.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:57.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7124
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:04:02.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     947
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:14.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:42.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.11
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.22
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.21
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.33
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.84
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.57
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.27
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:43.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7067.67
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:40.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.71
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:04.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.26
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.80
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:33.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5270.78
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:58.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45989
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869989
  j =  1                              :        399908026
  j =  2                              :            45981
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46350
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870350
  j =  1                              :        399907303
  j =  2                              :            46344
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:27.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:17.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :  3.5e-3

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:54.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.73e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:36.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:39.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.72
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.80
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.92
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.42
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.75
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.43
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.71
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  161.37
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17271.30
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.55
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.02
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.25
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.54
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.19
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.56
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.39
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.42
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.14
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.31
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.56
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.23
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.30
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.34
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.53
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.34
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.08
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.99
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.46
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.22
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.55
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.90
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4839.92
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.36
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.43
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.44
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.95
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.81
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.57
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.48
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:20.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.35
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:22.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.51e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.03
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.64
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.21
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:04.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.99
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10108.73
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10004.39
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:37.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5033.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:50.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.03
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4242.65
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11946.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.05
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.88
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999936257

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.72
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000028777

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   0.079
p-value of test                       :    0.47

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:49.57

 All tests were passed




Server wird beendet - Lösche Semaphor 114720794.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5393
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:55.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:04.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7129
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:55.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:00.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.07
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     959
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    2.35
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     262
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:15.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    3.21
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.20
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.63
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.03
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.07
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.23
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.14
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.44
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.92
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.42
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:43.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.09
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:00.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7317.64
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:44.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.98
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:03.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.94
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.65
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:34.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5103.27
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:07.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45719
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869719
  j =  1                              :        399908566
  j =  2                              :            45711
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45598
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869598
  j =  1                              :        399908804
  j =  2                              :            45598
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:28.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:58.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:54.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.62e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.94
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.22
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.88
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:42.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.57
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.27
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.15
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17543.28
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.97
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.27
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.64
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.64
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.13
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.98
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.18
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.96
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.65
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.02
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.86
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.40
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.99
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.49
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.08
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.30
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.71
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.18
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.78
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.70
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.65
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.10
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.98
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.06
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.68
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.65
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.86
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.83
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.46
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.79
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.24
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:21.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.78e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.45e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.60
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.82
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:03.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.89
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:04.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10170.04
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9805.24
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:40.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.02
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:47.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.07
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3994.84
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.09
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.99
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11913.10
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.09
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999991802

Normal statistic for number of bits   :  -0.065
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.70
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999950714

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 9.69e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.42
p-value of test                       :    0.9922

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:57.29

 All tests were passed




Server wird beendet - Lösche Semaphor 115736602.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.33

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5480
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:42.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:43.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:09.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:10.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:07.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:08.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.87
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    3.74
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.93
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:15.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.54
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:43.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.39
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.84
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.49
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.48
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.03
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.91
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7008.52
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.46
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.78
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.85
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:38.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5055.48
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:00.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45886
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869886
  j =  1                              :        399908230
  j =  2                              :            45882
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46056
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870056
  j =  1                              :        399907891
  j =  2                              :            46050
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:33.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9940


-----------------------------------------------
CPU time used                    :  00:02:20.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:49.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 8.20e-3
p-value of test                       :    0.9904

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:05.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:56.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  8.2e-3

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:37.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.29e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:24.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.38
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.86
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.78
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.17
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.05
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:52.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.74
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.32
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.83
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.52
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17107.43
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.11
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.02
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.37
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.23
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.93
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.55
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.58
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.91
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.96
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.04
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.81
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.71
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.91
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.22
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.15
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.51
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.62
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.20
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.08
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.70
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.54
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.01
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5120.68
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.61
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.35
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.23
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.94
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.52
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.93
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.47
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.53
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:20.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.46
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:19.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 9.82e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.14e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.74
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.10
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.92
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  154.42
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  2.1e-3

Anderson-Darling statistic = A2       :    3.90
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10296.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.37
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:04:18.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5001.17
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:55.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.70
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3959.05
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.06
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12236.19
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:01:33.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11732.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:32.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.89
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999961982

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.81
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999917612

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         : 9.44e-3
p-value of test                       :    0.50

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         : 5.44e-3
p-value of test                       :    0.50

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         : -6.96e-3
p-value of test                       :    0.50

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:24.98

 All tests were passed




Server wird beendet - Lösche Semaphor 116621338.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:48.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:55.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7152
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:07.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:07.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:00.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:05.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.77
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    4.60
p-value of test                       :  4.5e-3

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:15.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9968

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:44.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.63
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.70
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.14
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.04
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.33
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.97
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  370.86
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1494.32
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:03.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7001.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:08.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.85
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.61
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.31
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:00.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46015
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870015
  j =  1                              :        399907971
  j =  2                              :            46013
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45491
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869491
  j =  1                              :        399909023
  j =  2                              :            45481
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:30.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:19.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:08.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:57.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :  1.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:37.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.74e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.83
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.94
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.93
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.20
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.10
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.48
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17516.11
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.88
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   59.35
p-value of test                       :  6.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.32
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.06
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.30
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.55
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.17
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.92
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.36
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.61
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.85
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.88
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.47
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.85
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.37
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.43
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.43
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.92
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  444.99
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4854.68
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.11
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.40
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.18
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.04
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5164.37
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.34
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.49
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.10
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   -0.82
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:21.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.32
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:20.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.13e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 8.01e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.00e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.43
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.19
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:03.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:03.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.33
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10101.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:04:11.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.43
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:52.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:53.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.68
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4006.99
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11979.72
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.49
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.51
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000040648

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.31
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999944018

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:57.34

 All tests were passed




Server wird beendet - Lösche Semaphor 117669914.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5470
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:54.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4475
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7106
p-value of test                       :    0.9936


-----------------------------------------------
CPU time used                    :  00:03:04.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:04.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:55.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:00.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.24
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     640
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:14.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.69
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.41
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.38
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.98
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.71
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  389.00
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:43.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:02.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7064.91
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.97
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.02
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.31
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.68
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:35.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4930.04
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:00.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45798
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869798
  j =  1                              :        399908410
  j =  2                              :            45786
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45923
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869923
  j =  1                              :        399908160
  j =  2                              :            45911
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:27.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:18.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:58.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:36.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.08e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.55
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.47
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.33
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.45
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.63
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.09
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:44.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.51
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.73
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.26
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17334.79
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.92
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.28
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.24
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.42
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.83
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.81
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.74
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.03
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.02
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.31
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.59
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.69
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.70
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.39
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.64
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.56
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.92
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.36
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4820.12
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.64
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.77
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.23
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.75
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.74
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.50
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.87
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:34.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.94
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   0.021
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:21.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.22
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   0.075
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:21.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.21e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.94e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.35
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.90
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.59
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:04.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:04.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9758.57
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.95
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:36.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4748.84
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:50.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4262.24
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.39
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11478.01
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11748.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.75
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000036229

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.12
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000065116

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    2.92
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :  8.1e-4    *****

Anderson-Darling statistic = A2       :    4.22
p-value of test                       :  7.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.72
p-value of test                       :  3.3e-3

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  2.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:22.04

 All tests were passed




Server wird beendet - Lösche Semaphor 118751258.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5281
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:54.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7172
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:04.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:05.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:55.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:01.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.50
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    4.67
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:02:14.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:42.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.37
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.08
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.95
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.68
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.61
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.87
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  477.62
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1496.85
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7187.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:41.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.57
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:03.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.58
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.97
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:34.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5137.86
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:01.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45819
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869819
  j =  1                              :        399908365
  j =  2                              :            45813
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45934
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869934
  j =  1                              :        399908136
  j =  2                              :            45926
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:28.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:18.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9973

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:45.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:00.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.27e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.59e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:32.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.91
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.45
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:40.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.87
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.27
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.49
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17250.33
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.10
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.45
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.74
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.83
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.46
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.19
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.93
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.00
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.90
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.51
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.42
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.51
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.70
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.17
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.61
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.48
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.27
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  119.88
p-value of test                       :  5.9e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.93
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.25
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4836.54
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.54
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.53
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:34.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.48
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.41
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.18
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.51
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.45
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.30
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :    3.00
p-value of test                       :  1.3e-3



-----------------------------------------------
CPU time used                    :  00:02:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.91
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:22.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.96
p-value of test                       :    0.02

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.60e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.60e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.13
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.34
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.59
p-value of test                       :  4.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  145.62
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:02:03.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.26
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:04.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10162.41
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10088.58
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.027
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:37.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.39
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.43
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:50.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4247.20
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.77
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.58
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12025.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.34
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999989840

Normal statistic for number of bits   :  -0.080
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.21
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000010750

Normal statistic for number of bits   :   0.085
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    2.70
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:30.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 C (L=1000, r=20)    5.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 119767066.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9949


-----------------------------------------------
CPU time used                    :  00:00:38.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5374
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:54.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:03.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:04.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:54.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:00.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.62
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:16.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.73
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:46.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.10
p-value of test                       :  9.2e-3

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.61
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  381.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:44.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.77
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:02.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7024.23
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.09
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:03.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.87
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.95
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:35.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5205.20
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:01.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45749
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869749
  j =  1                              :        399908504
  j =  2                              :            45745
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45735
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869735
  j =  1                              :        399908532
  j =  2                              :            45731
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  8.3e-3

Anderson-Darling statistic = A2       :    4.05
p-value of test                       :  8.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  3.7e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:28.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:18.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:00.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:36.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.71
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.16
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.95
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.44
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.32
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.99
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17257.43
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.58
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.96
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.94
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.05
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.71
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.06
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.75
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.03
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.78
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.48
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.34
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.26
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.25
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.23
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  106.55
p-value of test                       :  7.9e-3


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.51
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.53
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.53
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.77
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.22
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.56
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.61
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4904.68
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.31
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.86
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.64
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.05
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5167.72
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.44
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.53
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.66
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.28
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    1.62
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:21.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.57e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.51e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 5.29e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.22
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.48
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.50
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:03.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.67
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:04.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9894.65
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9808.11
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:42.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4993.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4992.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:50.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.85
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4243.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11773.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11709.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.12
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000217903

Normal statistic for number of bits   :    1.72
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.60
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000052711

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    2.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:08.30

 All tests were passed




Server wird beendet - Lösche Semaphor 120750106.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:48.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5615
p-value of test                       :  4.5e-3


-----------------------------------------------
CPU time used                    :  00:03:55.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4221
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:57.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:04.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:57.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:02.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.42
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:14.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:44.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.66
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.65
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.03
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.04
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.88
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.95
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.30
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:00.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7062.03
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.67
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:02.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.57
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   90.11
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:33.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5015.14
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:59.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45599
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869599
  j =  1                              :        399908803
  j =  2                              :            45597
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45801
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869801
  j =  1                              :        399908403
  j =  2                              :            45791
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:29.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.29e-3
p-value of test                       :    0.9916

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  6.8e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:54.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:33.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-5
p-value of test                       :    0.9915

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.07e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.16
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.98
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.55
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.39
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   64.11
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.17
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:46.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.31
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17536.36
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:48.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.53
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.82
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.52
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.77
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.21
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.60
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.11
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.07
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.67
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.97
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.65
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.37
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.77
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.34
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:40.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.49
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.32
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.39
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.09
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.88
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.30
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4847.46
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.53
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.28
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.06
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.22
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5227.65
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  448.57
p-value of test                       :  7.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.69
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.76
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:11.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.60
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    1.27
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:11.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
p-value of test                       :    0.9918

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.86
p-value of test                       :    0.97

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.78e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.03e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.15
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.14
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:53.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.67
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:54.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9847.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.97
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:20.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.54
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:31.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5027.00
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.03
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.46
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11621.27
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.72
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000087424

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.65
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999878501

Normal statistic for number of bits   :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.5e-3

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:56:23.67

 All tests were passed




Server wird beendet - Lösche Semaphor 121733146.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5451
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:41.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:35.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:34.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:54.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:54.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:00.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:00.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7137
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:52.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:58.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.96
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     960
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    3.89
p-value of test                       :  9.9e-3

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.89
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    3.52
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    2.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:10.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:40.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.87
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.55
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.11
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.35
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.54
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  386.45
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1387.37
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:01.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7105.82
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   48.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.47
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:03.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.12
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.91
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:34.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5031.07
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:59.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45823
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869823
  j =  1                              :        399908362
  j =  2                              :            45807
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45813
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869813
  j =  1                              :        399908379
  j =  2                              :            45803
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:29.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:53.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.37e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 6.81e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 9.03e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.061
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:33.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.55
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.65
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.45
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.42
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.89
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:41.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.32
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    4.41
p-value of test                       :  5.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   99.53
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17670.82
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.22
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.98
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.44
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.36
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.13
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.65
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.37
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.06
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.65
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.19
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.26
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.77
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:46.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.24
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.41
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.29
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.04
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.89
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.40
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.60
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.04
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.98
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.93
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.52
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.72
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4931.44
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.10
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.45
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.27
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    1.54
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:26.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.43
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:18.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.48e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.98e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :  9.7e-3

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.95
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.67
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.37
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:05.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:08.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10035.41
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.26
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.033
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:45.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.92
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.98
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.90
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11800.10
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11814.49
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.59
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000044737

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.55
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000074023

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    2.94
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:48.84

 All tests were passed




Server wird beendet - Lösche Semaphor 102465563.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1243
p-value of test                       :    0.9995    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334363
  j =  1                              :        599997514
  j =  2                              :             1243
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5492
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:42.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:34.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:54.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:54.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:01.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:01.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:52.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.04
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    4.14
p-value of test                       :  7.5e-3

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:10.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:39.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.90
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.01
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.52
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.20
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.60
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.82
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:43.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:01.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6860.43
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 9.14e-4
p-value of test                       :    0.9991    *****

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.43
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:04.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.47
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:47.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.24
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4991.19
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:01.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908068
  j =  2                              :            45963
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45879
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869879
  j =  1                              :        399908246
  j =  2                              :            45871
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:31.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:54.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.79e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.33e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.040
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:34.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.96
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.80
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.11
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:48.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.12
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:41.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.15
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.11
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  175.58
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17528.71
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.46
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.24
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.04
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.56
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.02
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.15
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.57
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.90
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.46
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.11
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.41
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.86
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.15
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.93
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.72
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.16
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.97
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.19
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.34
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.21
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5181.36
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.78
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.00
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.25
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.52
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.42
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.91
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.55
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.83
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:27.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.59
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:21.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.83e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 8.37e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.35
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.52
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.68
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:10.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.03
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:10.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.19
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9783.92
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:04:04.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5020.15
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.92
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.92
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.70
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11597.37
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11636.05
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.01
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000080989

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.89
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999897080

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :  -0.079
p-value of test                       :    0.53

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:27.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 102662171.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5432
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:44.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:37.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:34.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:54.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:01.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:01.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:52.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:58.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.21
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    3.54
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     822
p-value of test                       :    0.9956

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:15.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:43.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.04
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.74
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.09
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.12
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.42
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.10
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.33
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.64
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  483.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:01.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6894.12
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.80
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.76
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:04.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.58
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.20
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:33.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5131.23
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:55.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45941
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869941
  j =  1                              :        399908123
  j =  2                              :            45931
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45674
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869674
  j =  1                              :        399908655
  j =  2                              :            45668
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:30.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:17.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:44.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:55.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:33.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:31.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.086
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:33.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.76
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.39
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.00
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.78
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.55
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:42.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.30
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17420.36
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.56
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.35
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.64
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.77
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.04
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.18
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.61
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.00
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.91
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.79
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.44
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.91
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.03
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.42
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.76
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.78
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.01
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.41
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.66
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.21
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.17
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.15
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.01
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.19
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.74
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.48
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.05
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4858.98
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.67
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.63
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.37
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    1.61
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:26.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.51
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
p-value of test                       :    0.9939

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.21
p-value of test                       :    0.99

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.14
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.22
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.84
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:07.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.26
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:07.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9964.11
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9909.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.042
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:53.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:48.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4998.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4226.54
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4002.66
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11863.55
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11850.85
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.55
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999983798

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.37
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000011953

Normal statistic for number of bits   :   0.094
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:23.12

 All tests were passed




Server wird beendet - Lösche Semaphor 103612443.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1253
p-value of test                       :    0.9988

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334373
  j =  1                              :        599997494
  j =  2                              :             1253
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:49.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4435
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:35.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:53.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:54.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:01.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:01.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:54.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7566
p-value of test                       :  2.0e-3


-----------------------------------------------
CPU time used                    :  00:03:56.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:15.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:40.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.40
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.17
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.86
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.17
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.79
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1401.75
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7021.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.67
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:09.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.62
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.62
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:37.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.49
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:02.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46014
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870014
  j =  1                              :        399907976
  j =  2                              :            46006
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45767
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869767
  j =  1                              :        399908470
  j =  2                              :            45759
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:30.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :  1.9e-3

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:03.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.28e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 5.61e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.17e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:44.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.92
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.87
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.49
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.09
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.69
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.00
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.44
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.38
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17385.18
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.60
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.72
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.20
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.73
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.34
p-value of test                       :    0.9906


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.41
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.39
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.29
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.63
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :   96.17
p-value of test                       :    0.9995    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.33
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.93
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.41
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.11
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.17
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.77
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.91
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.46
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.73
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.06
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.09
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.31
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.72
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.32
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.12
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.50
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4856.70
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.96
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.51
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.28
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :   -0.82
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.98
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    2.17
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:02:25.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.60
p-value of test                       :  2.8e-4    *****

Anderson-Darling statistic = A2       :    5.57
p-value of test                       :  1.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.10
p-value of test                       :    0.02

Sample variance                       :    2.70
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.0e-3

Anderson-Darling statistic = A2       :    5.37
p-value of test                       :  2.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.90
p-value of test                       :  1.9e-3

Sample variance                       :    0.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.69e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.40e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.32
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.47
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:04.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9946

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.39
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:04.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.34
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.099
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:04:21.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.88
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:52.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4738.98
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:54.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.95
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4220.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11832.54
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:31.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12143.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.89
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000107965

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.09
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000048268

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :  -0.031
p-value of test                       :    0.51

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   0.097
p-value of test                       :    0.46

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:10.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 H (L=1000, r=0)     0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 104628251.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:51.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:48.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:37.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:36.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:53.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:04.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:55.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:55.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.68
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     643
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:13.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    3.80
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:43.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.71
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.01
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.23
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.43
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  284.66
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.71
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1362.93
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:06.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7044.01
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.89
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.23
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:08.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.08
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.31
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:37.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4964.86
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:55.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45955
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869955
  j =  1                              :        399908098
  j =  2                              :            45939
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45876
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869876
  j =  1                              :        399908255
  j =  2                              :            45862
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:29.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:19.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9918


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :  2.5e-3

Kolmogorov-Smirnov- statistic = D-    : 5.18e-3
p-value of test                       :    0.9943

Anderson-Darling statistic = A2       :    5.24
p-value of test                       :  2.3e-3


-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:03.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:57.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 5.52e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.55
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.87
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.94
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.35
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.62
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.42
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.28
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.78
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.05
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17500.91
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.44
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.53
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.58
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.90
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.24
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.67
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.61
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.31
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.23
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.94
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.33
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.61
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.04
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.12
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.46
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.27
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.03
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.38
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.41
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.47
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5111.48
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.41
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.07
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.60
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.23
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.81
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.65
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.27
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.02
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :  -0.069
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:22.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.02
p-value of test                       :    0.02

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.72
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.16
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.34
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:08.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.39
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:08.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10220.87
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.74
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:04:17.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.34
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:53.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5005.23
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.42
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.11
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11474.90
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:32.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.06
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:31.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.44
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999744446

Normal statistic for number of bits   :   -2.02
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.28
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000019957

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         : -6.96e-3
p-value of test                       :    0.50

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.89
p-value of test                       :    0.97

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:53.10

 All tests were passed




Server wird beendet - Lösche Semaphor 105873435.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:51.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:50.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:39.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:39.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:02.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:01.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:54.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:59.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:50.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    2.97
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     650
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.00
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:17.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.06
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:44.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.56
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.60
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.35
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.74
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.06
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.26
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.45
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:03.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7153.30
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.02
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.94
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:04.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.53
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.66
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5124.77
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:56.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46358
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870358
  j =  1                              :        399907287
  j =  2                              :            46352
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46056
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870056
  j =  1                              :        399907892
  j =  2                              :            46048
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:28.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.71e-3
p-value of test                       :    0.9982

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9930


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:54.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:32.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.09e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:40.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:39.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.10
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.68
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   99.92
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.68
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.39
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.56
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.69
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.93
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17500.15
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.70
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.13
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.00
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.15
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.04
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.21
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.60
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.89
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.43
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.10
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.87
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  199.13
p-value of test                       :  2.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.79
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.08
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.80
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.37
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.22
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   46.44
p-value of test                       :    0.9950


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.80
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.19
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.77
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.03
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.68
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.47
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.62
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.18
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.68
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.33
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.85
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:24.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.22
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:25.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
p-value of test                       :    0.9945

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.86
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.74
p-value of test                       :  3.1e-3

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.48e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 7.86e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.68e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 7.89e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.65
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.39
p-value of test                       :    0.9944

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:08.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.61
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:08.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.87
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9875.66
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.038
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:04:06.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.07
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:52.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.99
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:52.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.51
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3922.40
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.88
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11880.61
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.65
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999947780

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.31
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000139297

Normal statistic for number of bits   :    1.10
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.16
p-value of test                       :    0.9976

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:11.23

 All tests were passed




Server wird beendet - Lösche Semaphor 107151387.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:50.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4439
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:38.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7169
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:38.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:54.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:01.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:00.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:53.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:57.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:16.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:44.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.56
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.46
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.91
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.04
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.99
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.29
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.15
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.10
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:06.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6990.86
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.38
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:06.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.16
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.61
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:35.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5136.85
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:11.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45865
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869865
  j =  1                              :        399908273
  j =  2                              :            45859
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46010
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870010
  j =  1                              :        399907981
  j =  2                              :            46008
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:28.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  9.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:16.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.93e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.04e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:37.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.73
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.15
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.75
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.41
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.00
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.26
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.69
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17319.36
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:51.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.90
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.01
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.41
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.11
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.35
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.86
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.92
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.69
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.75
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   36.01
p-value of test                       :  4.6e-3


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.95
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.36
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  440.73
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.09
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.24
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.53
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.92
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.59
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  170.27
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.44
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.67
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.93
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5092.76
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.98
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.77
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.20
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.80
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4899.42
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.11
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.05
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.56
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:26.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.39
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:25.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.34e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 5.66e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.62
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.73
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.20e-3
p-value of test                       :    0.9945

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.4e-3

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  249.29
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:05.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.95
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9779.01
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.60
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:04:11.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4752.79
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:50.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.27
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.98
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11725.55
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11932.51
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:30.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.99
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000045757

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.61
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000016879

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:25.29

 All tests were passed




Server wird beendet - Lösche Semaphor 108068891.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1476
p-value of test                       :  1.5e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334596
  j =  1                              :        599997048
  j =  2                              :             1476
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5326
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:51.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7576
p-value of test                       :  1.4e-3


-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:02.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:03.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:55.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:59.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:50.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.88
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    2.47
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:16.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:43.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.21
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.07
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.71
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.50
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.19
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.76
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.57
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.75
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1486.79
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7087.34
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.74
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:04.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.79
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.67
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5034.14
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:08.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45954
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869954
  j =  1                              :        399908093
  j =  2                              :            45952
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45740
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869740
  j =  1                              :        399908528
  j =  2                              :            45724
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:27.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  4.7e-3

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:17.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:54.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:33.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.68e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 3.05e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.079
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:35.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.04
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.56
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.43
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.53
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.72
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.51
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.67
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17242.43
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.30
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.35
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.80
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.91
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.07
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.72
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.94
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.16
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.04
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.24
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.92
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.83
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.67
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.82
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.49
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.73
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.52
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.60
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.61
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.33
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.26
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.58
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.04
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.28
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.73
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.12
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:21.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.67
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 9.28e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 9.13e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.45
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.00
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:05.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:06.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10237.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9883.72
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:44.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.50
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5115.93
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.24
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.50
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11724.92
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11644.73
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.31
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000029347

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.05
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999973700

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:53.23

 All tests were passed




Server wird beendet - Lösche Semaphor 109051931.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5494
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:50.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:39.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4217
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:04.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:03.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:53.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:00.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:14.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:45.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.26
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.03
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  385.16
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.60
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6893.61
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:41.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.34
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:03.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.98
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.64
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:32.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5030.06
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:03.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45754
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869754
  j =  1                              :        399908495
  j =  2                              :            45748
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908198
  j =  2                              :            45901
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:28.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:18.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:02.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:34.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.88e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.62e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.43
p-value of test                       :    0.9925

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:33.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.77
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.60
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.22
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.18
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.79
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.55
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:40.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.43
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.53
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17558.68
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.96
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.68
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.74
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.49
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.32
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.40
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.77
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.75
p-value of test                       :    0.9941


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.03
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.53
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.60
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.96
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.96
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.79
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.11
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.99
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.46
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.48
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.14
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.20
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.99
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.58
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.53
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.77
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.26
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.74
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.54
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.67
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.86
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :  -0.078
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:23.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.15
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :  -0.064
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.85e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 7.02e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 3.24e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.43
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.90
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:07.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.45
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.044
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:39.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4715.04
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5038.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:50.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.27
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11612.22
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.94
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000169711

Normal statistic for number of bits   :    1.34
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.47
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999968159

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:38.87

 All tests were passed




Server wird beendet - Lösche Semaphor 110067739.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5477
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:52.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4467
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4465
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:04.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:04.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:54.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:00.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:46.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:11.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    2.69
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.67
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.28
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.72
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.20
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.48
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.10
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.07
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.77
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.42
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.02
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:45.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.38
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7210.29
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:42.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.36
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:04.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.56
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.11
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5027.15
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:59.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46100
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870100
  j =  1                              :        399907802
  j =  2                              :            46096
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45276
p-value of test                       :    0.9976


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869276
  j =  1                              :        399909448
  j =  2                              :            45276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:27.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:17.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9912

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:58.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:31.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:32.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.22
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.67
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:48.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.79
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   46.79
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:37.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.33
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.92
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.42
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17242.88
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.15
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.86
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.66
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.29
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.76
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.30
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.53
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.22
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.99
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.92
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.64
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.96
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.67
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.93
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.98
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.60
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.37
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.52
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.37
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.35
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4809.77
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  299.38
p-value of test                       :    0.9989


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.82
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.34
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.55
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.47
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.72
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.46
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.12
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    0.86
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:22.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.07
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :  -0.019
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 2.76e-4
p-value of test                       :    0.9997    *****

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -2.11
p-value of test                       :    0.98

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.38e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.98
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.59
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.20
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:05.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.21
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:07.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10269.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10318.85
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.29
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:38.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.08
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.38
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:51.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4319.74
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.50
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11952.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12044.20
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.41
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000007483

Normal statistic for number of bits   :   0.059
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.94
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000135004

Normal statistic for number of bits   :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:55.04

 All tests were passed




Server wird beendet - Lösche Semaphor 110985243.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5527
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:54.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:04.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:53.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:59.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    2.87
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:13.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:40.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.58
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.20
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.37
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.65
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.60
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  506.34
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:01.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7141.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:42.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.26
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.03
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:07.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.45
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.78
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4971.18
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:14.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46037
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870037
  j =  1                              :        399907929
  j =  2                              :            46031
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45800
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869800
  j =  1                              :        399908403
  j =  2                              :            45794
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:28.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:17.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:45.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-5
p-value of test                       : 1 -  1.8e-5    *****

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :  4.6e-4    *****

Anderson-Darling statistic = A2       :    4.78
p-value of test                       :  3.7e-3


-----------------------------------------------
CPU time used                    :  00:02:01.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.081
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:35.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.82
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:47.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.92
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.65
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.16
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.51
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.71
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.01
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.40
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.76
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17064.56
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.79
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.50
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.52
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.31
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.21
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.42
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.41
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.45
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.03
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.92
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.38
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.49
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.15
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.92
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.57
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.37
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.21
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.68
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.06
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.47
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.11
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.97
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.86
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.96
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.63
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.68
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.96
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.19
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.61
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:21.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.45
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:22.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.70e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.43e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 4.93e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.92
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.88
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.95
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:03.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.50
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:06.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9762.88
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9731.63
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:42.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.40
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.15
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.06
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12016.15
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11666.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.29
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999996923

Normal statistic for number of bits   :  -0.024
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.89
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000083653

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:04.53

 All tests were passed




Server wird beendet - Lösche Semaphor 111935515.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5345
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:56.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:04.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7489
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:04.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:54.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7138
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:59.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.04
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:13.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.40
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.57
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:40.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.51
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.53
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.44
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.69
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.85
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.72
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1332.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6846.14
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.04
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.38
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:04.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.07
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.43
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4859.16
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:03.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46307
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870307
  j =  1                              :        399907391
  j =  2                              :            46297
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45716
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869716
  j =  1                              :        399908571
  j =  2                              :            45710
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:27.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:18.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:33.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 2.92e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.63
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:01:36.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.45
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:01:36.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.23
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.04
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:47.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.15
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.64
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.44
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:36.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.98
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.49
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.75
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17212.09
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.84
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.09
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.81
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.64
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.93
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.18
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.12
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.21
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.89
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.99
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.73
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.46
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.48
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.40
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.22
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.45
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.52
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  171.85
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.60
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.67
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.09
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.71
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.03
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.01
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.27
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.11
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.96
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.60
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.64
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:21.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   28.39
p-value of test                       :  4.8e-3


-----------------------------------------------
Normal statistic for number of jumps  :    1.36
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:20.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.17e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.54e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.66
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.69
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.33
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:07.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
p-value of test                       :    0.9912

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10294.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9814.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:40.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.89
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.84
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.17
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.72
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.87
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11834.24
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.41
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999915557

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.22
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000155200

Normal statistic for number of bits   :    1.23
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:40.40

 All tests were passed




Server wird beendet - Lösche Semaphor 112918555.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5550
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:55.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:41.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:05.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:55.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:59.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:46.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.82
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:11.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:40.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.37
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.13
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.02
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.71
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.08
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7050.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.36
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:05.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.69
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.26
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:31.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5132.32
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:57.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46304
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870304
  j =  1                              :        399907393
  j =  2                              :            46302
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45615
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869615
  j =  1                              :        399908777
  j =  2                              :            45601
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:26.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9946

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:01.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:55.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.60e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:37.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.87
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:48.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.49
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.61
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.62
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.15
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   97.91
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17215.55
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.66
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.82
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.63
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.43
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.99
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.93
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.65
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.36
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.95
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.84
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.22
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.13
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.97
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.65
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.97
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.57
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.71
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.55
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.17
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.87
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.24
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.55
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.04
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.74
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.86
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.01
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.36
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4877.15
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.06
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.26
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.79
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    0.51
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.79
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:21.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.96e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.20
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.08
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:03.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
p-value of test                       :    0.9936

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10141.67
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9797.20
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:51.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.67
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.01
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11963.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11645.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.35
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999970610

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.90
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999945452

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  6.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.89
p-value of test                       :  3.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.93
p-value of test                       :    0.9983

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:14.53

 All tests were passed




Server wird beendet - Lösche Semaphor 113901595.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5483
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:57.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:06.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:06.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:56.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:02.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.42
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    2.53
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    2.59
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:13.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.54
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.54
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.24
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.63
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.56
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.60
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.62
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:44.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7194.50
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.60
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.69
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:05.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   23.18
p-value of test                       :  3.1e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.18
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5127.70
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:23.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45213
p-value of test                       :    0.9991    *****


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869213
  j =  1                              :        399909576
  j =  2                              :            45209
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46671
p-value of test                       :  1.2e-4    *****


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870671
  j =  1                              :        399906661
  j =  2                              :            46665
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
p-value of test                       :    0.9938

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:27.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:18.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :  1.4e-3

Kolmogorov-Smirnov- statistic = D-    : 5.13e-4
p-value of test                       :    0.9995    *****

Anderson-Darling statistic = A2       :    7.58
p-value of test                       :  1.9e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       : 1 -  4.3e-5    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:55.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:33.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.047
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.55
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:47.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.71
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.66
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.85
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.55
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.00
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.52
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.22
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.39
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17520.64
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   16.53
p-value of test                       :    0.9978


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.50
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.06
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.06
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.11
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.93
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.38
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.32
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.47
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.42
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.26
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.62
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.52
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.01
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.18
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.65
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.25
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.49
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.54
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.26
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.32
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.13
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.33
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.39
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.59
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.64
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5174.51
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.50
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  248.03
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   32.32
p-value of test                       :  1.2e-3


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:22.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.02
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:21.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    2.69
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.55e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.17e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 8.13e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.66
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.51
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.46
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:05.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.64
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10098.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10108.08
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:36.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.15
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:47.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.44
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:50.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4291.71
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11793.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11935.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.91
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000086506

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.92
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999986348

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:59.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 40  Permutation, t = 3              3.1e-4
 44  CollisionPermut, r = 0          0.9991 
 45  CollisionPermut, r = 10         1.2e-4
 48  MaxOft, t = 24                 1 -  4.3e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 114917403.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:50.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1259
p-value of test                       :    0.9979

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334379
  j =  1                              :        599997482
  j =  2                              :             1259
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:57.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4215
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:06.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:06.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:55.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:00.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    3.02
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     254
p-value of test                       :    0.9964

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:16.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.36
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:39.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.02
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.05
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.27
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.50
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.97
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.29
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.50
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:04.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6959.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.24
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.71
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:05.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.18
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.66
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5035.37
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:02.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45572
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869572
  j =  1                              :        399908860
  j =  2                              :            45564
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46058
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870058
  j =  1                              :        399907886
  j =  2                              :            46054
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:26.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:17.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:03.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:54.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 8.38e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.068
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:38.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.09
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.00
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.47
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.69
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:37.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.49
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.14
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   99.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17643.31
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.64
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.37
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.24
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.88
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.73
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.43
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.74
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.05
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.92
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.56
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.11
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.73
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   47.42
p-value of test                       :    0.9931


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.40
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.19
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.93
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.34
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.21
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.14
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.02
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4867.81
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.48
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.09
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.30
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.66
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.79
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.40
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.63
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    1.28
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:23.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.43
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:22.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-3
p-value of test                       :    0.9982

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    2.15
p-value of test                       :    0.02

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.92e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.42e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   23.28
p-value of test                       :  3.0e-3

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.77
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:06.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9907.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.37
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:41.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.59
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.70
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:51.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.81
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4010.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11703.31
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11751.44
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.04
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999829604

Normal statistic for number of bits   :   -1.35
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.69
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999971336

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   0.066
p-value of test                       :    0.47

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.93

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:49.25

 All tests were passed




Server wird beendet - Lösche Semaphor 115933211.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5432
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:57.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:43.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:07.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:08.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:55.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:00.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.89
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    3.60
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    3.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:15.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:39.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.82
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.61
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.68
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.28
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.25
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.86
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.42
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.36
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:45.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1364.21
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:03.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7131.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:43.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.41
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.15
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:02.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   16.28
p-value of test                       :  6.1e-3


-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.69
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:31.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4806.14
p-value of test                       :    0.9906


-----------------------------------------------
CPU time used                    :  00:01:11.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:05.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45801
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869801
  j =  1                              :        399908403
  j =  2                              :            45791
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45780
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869780
  j =  1                              :        399908442
  j =  2                              :            45776
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:26.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:54.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.46e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.021
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.08
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:47.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.92
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.17
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.35
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.07
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17029.94
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.42
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.80
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.50
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.56
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.43
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.17
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.61
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.38
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.80
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.43
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.11
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.00
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.79
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.20
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.58
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.01
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.87
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.06
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.37
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.02
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.58
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.93
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.97
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.73
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.40
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.33
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.42
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:24.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.88
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :  5.3e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.67
p-value of test                       :  4.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.63
p-value of test                       :    0.9957

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.48e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.23e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 7.48e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.19
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.63
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.61
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:06.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9875.52
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10014.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:40.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.85
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4745.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4240.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4014.78
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11824.09
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11738.03
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.09
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000035056

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.06
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000006010

Normal statistic for number of bits   :   0.048
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:31.25

 All tests were passed




Server wird beendet - Lösche Semaphor 116949019.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5353
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:57.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:42.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4451
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7472
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:06.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:56.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:00.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:15.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:45.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.48
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.57
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.33
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.02
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.67
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7041.82
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:43.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.22
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:02.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.83
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.10
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.99
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:19.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45821
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869821
  j =  1                              :        399908361
  j =  2                              :            45815
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45964
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869964
  j =  1                              :        399908079
  j =  2                              :            45950
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 4.29e-3
p-value of test                       :    0.9949

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:26.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:18.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  7.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:54.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:34.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.13
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.67
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.03
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.65
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.64
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.96
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.05
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17455.30
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.13
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.75
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.58
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.17
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.79
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.66
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.10
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.62
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.86
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.69
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.84
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.22
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.94
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.01
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.08
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.67
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.41
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.20
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.97
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.45
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.30
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.65
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.75
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.94
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.39
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.84
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.78
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.24
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.39
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.14
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.07
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :  -0.069
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:22.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.35e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 9.55e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 4.14e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.09
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.53
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.42
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:05.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10188.86
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10102.55
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:42.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4708.11
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.34
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11759.15
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12127.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.98
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000083005

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.71
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999907268

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-3
p-value of test                       :    0.9977

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.57
p-value of test                       :  5.1e-3

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:02.54

 All tests were passed




Server wird beendet - Lösche Semaphor 117932059.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5338
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:58.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:42.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:58.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:06.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:05.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:57.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:01.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.14
p-value of test                       :    0.9991    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     265
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:16.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.32
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    2.67
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:42.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.21
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.20
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.55
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.00
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.60
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.31
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.17
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:44.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7151.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.36
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:02.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.27
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.05
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:32.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4867.10
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:18.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45846
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869846
  j =  1                              :        399908316
  j =  2                              :            45830
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45673
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869673
  j =  1                              :        399908661
  j =  2                              :            45659
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:25.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9976


-----------------------------------------------
CPU time used                    :  00:02:17.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:45.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:54.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.81e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 9.02e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:22.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:34.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.073
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.99
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.38
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:48.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.60
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.91
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:37.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.28
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.79
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17327.43
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.53
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.80
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.74
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.79
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.52
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.62
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.58
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.12
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.45
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.87
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.22
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.12
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.63
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.85
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.76
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.69
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   95.92
p-value of test                       :    0.9963


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.62
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.57
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.85
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.69
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.40
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.63
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.24
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.74
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.81
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.44
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.60
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.25
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.68
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    0.86
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.69
p-value of test                       :    0.95

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 5.57e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.09e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.00
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.20
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.89
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:05.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.51
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:05.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.81
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.16
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:40.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4753.05
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.50
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.31
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11657.31
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11709.76
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.64
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999976898

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.90
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999983495

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:03.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP1, t = 3          0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 118947867.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5507
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:58.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4454
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4439
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:58.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:05.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:06.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:01.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.25
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.21
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:15.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.29
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.12
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.85
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.69
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.40
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.96
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.41
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.74
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:44.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.53
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6968.99
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.56
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.18
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:02.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.17
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  157.65
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5047.80
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45802
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869802
  j =  1                              :        399908401
  j =  2                              :            45792
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45879
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869879
  j =  1                              :        399908242
  j =  2                              :            45879
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:25.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  8.1e-3

Anderson-Darling statistic = A2       :    3.68
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:17.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:00.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:54.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:32.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:33.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.086
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:34.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.00
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.75
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.63
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.55
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.53
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.66
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17237.16
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.12
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.02
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.12
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.77
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.75
p-value of test                       :  9.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   43.18
p-value of test                       :  9.5e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.62
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.79
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.83
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.76
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.26
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.77
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.43
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.58
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.81
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.06
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.24
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.88
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.32
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.50
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.92
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.12
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.45
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  449.82
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.28
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.52
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.57
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.73
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:22.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.26
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.46e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 4.49e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.80
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.33
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.63
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:05.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.81
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9958.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10223.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:42.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.57
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.46
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.89
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11734.31
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.69
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000293902

Normal statistic for number of bits   :    2.32
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.87
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000130912

Normal statistic for number of bits   :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:49.14

 All tests were passed




Server wird beendet - Lösche Semaphor 119963675.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5405
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:59.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:42.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4450
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:05.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:08.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:58.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:01.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.93
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     939
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    2.23
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:15.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.06
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:43.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.50
p-value of test                       :    0.9994    *****

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.33
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.46
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.26
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.20
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1378.16
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:01.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7068.05
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:02.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.59
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.41
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:31.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:16.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45846
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869846
  j =  1                              :        399908312
  j =  2                              :            45838
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46116
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870116
  j =  1                              :        399907774
  j =  2                              :            46104
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:26.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:17.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 2.88e-3
p-value of test                       :    0.9970

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:53.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.81e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.71e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.28e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:32.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.06
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.10
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.39
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.89
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.64
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.96
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:40.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.12
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.35
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.063
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.95
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17464.98
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.47
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.97
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.09
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.67
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.76
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.59
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.69
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.19
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.17
p-value of test                       :    0.9919


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.17
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.57
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.55
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.38
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.61
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.22
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.64
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.19
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.77
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.26
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.41
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.35
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.10
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.16
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.49
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.99
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.97
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.40
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.58
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.20
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.59
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:22.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.49
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:21.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.5e-3

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.18
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    2.96
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 3.37e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 6.02e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.07
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.67
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:03.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.14
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:04.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10078.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.20
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:39.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9971

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.32
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5057.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:49.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.43
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11830.97
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11862.35
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.34
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999966767

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.19
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000031606

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.99
p-value of test                       :    0.98

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:45.98
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 26  SimpPoker, r = 0                0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 120979483.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5369
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:42.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:35.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:33.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:54.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:00.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:01.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7526
p-value of test                       :  7.9e-3


-----------------------------------------------
CPU time used                    :  00:03:52.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:58.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.75
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:11.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:37.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.56
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.16
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.32
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.77
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.42
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.15
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.80
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1305.02
p-value of test                       :    0.9943

-----------------------------------------------
CPU time used                    :  00:02:00.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7083.90
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:44.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.17
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:03.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.21
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.17
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4960.77
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:05.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45821
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869821
  j =  1                              :        399908361
  j =  2                              :            45815
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45932
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869932
  j =  1                              :        399908137
  j =  2                              :            45930
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:29.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:18.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:53.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:33.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.18e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.32e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.050
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.78
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.55
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.61
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.58
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:48.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.55
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.75
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.04
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.28
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.62
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17545.57
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.84
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.57
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.24
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.31
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.69
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.43
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.05
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.10
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.15
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.18
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.74
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.66
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.72
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.62
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.47
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:47.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.12
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.65
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.02
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.90
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.40
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:47.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.81
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.10
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.53
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.84
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.03
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.63
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.38
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.72
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.91
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.47
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:17.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.99e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.81
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.81
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.13
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:07.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9957

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:08.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9904.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.2e-3

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10299.91
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:46.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.57
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:50.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.78
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4257.02
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11719.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.95
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.16
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000074818

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.08
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000087769

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.059
p-value of test                       :    0.52

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:56.80

 All tests were passed




Server wird beendet - Lösche Semaphor 102498332.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5296
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:44.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4215
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:36.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:34.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:52.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:59.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:00.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:51.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7053
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:03:55.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    2.45
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    4.23
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:02:12.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    4.06
p-value of test                       :  8.2e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     120
p-value of test                       :    0.9934

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:43.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.05
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.31
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.20
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1595.90
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:02:05.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7048.95
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.48
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:19.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.08
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.54
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5095.42
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45636
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869636
  j =  1                              :        399908734
  j =  2                              :            45624
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45864
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869864
  j =  1                              :        399908275
  j =  2                              :            45858
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:29.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:17.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:01.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:53.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.50e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.34
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.97
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.78
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.79
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.96
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.73
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.03
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:44.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.32
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.62
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.41
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17213.19
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.58
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.06
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.77
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.05
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.36
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.30
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.60
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.20
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.14
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.99
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.14
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.52
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.85
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.81
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.47
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.75
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.37
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.84
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.50
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.49
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4879.61
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.70
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.25
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:34.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.93
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.94
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5100.65
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  318.79
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.97
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:34.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.61
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -1.69
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.10
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:26.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
p-value of test                       :    0.9918

Anderson-Darling statistic = A2       :    3.77
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.76
p-value of test                       :    0.9971

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 4.16e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.20e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.57
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.62
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.84
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.23
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:05.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9889.35
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10122.08
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:04:17.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4933.48
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:50.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.82
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:53.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.83
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.02
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.00
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12076.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.65
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999933047

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.51
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000107392

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.82
p-value of test                       :    0.97

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:14.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 21  BirthdaySpacings, t = 16        0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 102858780.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:47.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:37.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:37.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:02.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:03.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:52.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:58.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:13.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9957

Stat. AD after spacings (mNP2-S)      :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:42.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.46
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.27
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.08
p-value of test                       :  9.2e-3

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.44
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.18
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1367.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:59.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7072.95
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.70
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:03.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.63
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  150.44
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5033.41
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:19.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46100
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870100
  j =  1                              :        399907804
  j =  2                              :            46092
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46025
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870025
  j =  1                              :        399907957
  j =  2                              :            46011
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:28.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:18.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:01.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:54.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:32.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.21e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.33e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    3.48
p-value of test                       :  2.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:35.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.49
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.71
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.48
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.86
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.02
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.45
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:29.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.52
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17451.43
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:51.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.67
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.80
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.25
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.18
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.30
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.31
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.59
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.06
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.42
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.71
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.02
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.26
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.34
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.99
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.88
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.63
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.94
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.77
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.77
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.38
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.24
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.14
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.47
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.14
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.40
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.72
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.39
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.86
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.25
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.65
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:26.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.26
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    0.16
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:26.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.38e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 4.98e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.76e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 3.39e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.67
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.66
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:06.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.55
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:08.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.24
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.63
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:41.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5076.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.80
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:50.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.08
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4309.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11934.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11683.60
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:30.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.71
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000055630

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.60
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999971729

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.84
p-value of test                       :    0.97

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:35.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 55  SampleCorr, k = 1               2.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 104103964.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:52.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:47.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7145
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:37.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:05.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:00.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:03.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9919

Test on the Nm values of W_{n,i}(mNP1):    2.56
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     348
p-value of test                       :  3.6e-3

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:11.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.18
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:42.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.21
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:11.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.52
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.94
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.21
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:08.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7119.41
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:57.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.24
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:17.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.25
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.60
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4834.88
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:01.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45667
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869667
  j =  1                              :        399908670
  j =  2                              :            45659
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45857
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869857
  j =  1                              :        399908289
  j =  2                              :            45851
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.20e-3
p-value of test                       :    0.9987

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:30.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:18.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:09.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:37.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.61e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.67
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.35
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.68
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.54
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.58
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.76
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.84
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.55
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17439.56
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.32
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.70
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.76
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.88
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.74
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.44
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.25
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.83
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.21
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.53
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.36
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.99
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.75
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.67
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.10
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.39
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.77
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.59
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.80
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.88
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.08
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.17
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.39
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.42
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.22
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.14
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.81
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.78
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.11
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.81
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :    1.64
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:26.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.63
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:26.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.87e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.57
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.45
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.96
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:08.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:07.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9930.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10063.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:04:35.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.18
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:00.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.09
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11758.41
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:37.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11570.73
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:37.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.22
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000058372

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.84
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999832688

Normal statistic for number of bits   :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:35.94

 All tests were passed




Server wird beendet - Lösche Semaphor 105021468.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5482
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:51.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:37.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:01.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7100
p-value of test                       :    0.9947


-----------------------------------------------
CPU time used                    :  00:03:55.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:02.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    3.96
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:02:13.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.53
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.73
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.83
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  190.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  368.70
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:43.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.07
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:59.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7203.78
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.75
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.28
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:02.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.47
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.54
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5198.64
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:01.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46096
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870096
  j =  1                              :        399907811
  j =  2                              :            46090
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45823
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869823
  j =  1                              :        399908358
  j =  2                              :            45815
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:27.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:18.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:00.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.79e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.50e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:32.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.74
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.63
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.85
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.37
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:39.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.74
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.22
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.17
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.79
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17441.56
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.41
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.71
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.74
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.17
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.05
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.94
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.17
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.46
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.30
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.52
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.92
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.21
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.12
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.69
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.37
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.15
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.71
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.09
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.10
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.08
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.53
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.68
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.93
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.06
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.66
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.90
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.33
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.01
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -2.02
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:25.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.86
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :  -0.033
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:25.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.76e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 4.61e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.57
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.25
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.88
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:05.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.23
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:06.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.14
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.85
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:46.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.72
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.84
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3949.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11745.05
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11922.37
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.12
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000128965

Normal statistic for number of bits   :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.43
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000014074

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.081
p-value of test                       :    0.47

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.95e-3
p-value of test                       :    0.9970

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.05
p-value of test                       :    0.02

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:59.92

 All tests were passed




Server wird beendet - Lösche Semaphor 106266652.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:52.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:38.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:01.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:04.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:54.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:02.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    3.62
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     181
p-value of test                       :  7.6e-3

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.99
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.74
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.41
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.84
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.42
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.20
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.39
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:44.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6884.15
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.39
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.34
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:02.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.72
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.72
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:34.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4903.44
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:59.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46098
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870098
  j =  1                              :        399907808
  j =  2                              :            46090
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46210
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870210
  j =  1                              :        399907584
  j =  2                              :            46202
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:27.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:53.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:32.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 8.71e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.092
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.74
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:35.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.72
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.12
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:47.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.69
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.05
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.54
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.10
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.61
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17592.32
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.88
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.29
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.31
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.66
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.87
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.54
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.85
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.24
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.76
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.84
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.54
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.74
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  573.85
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.39
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.26
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.63
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.12
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.56
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.92
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.79
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.49
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4882.95
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.99
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.65
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.78
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.61
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.14
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.06
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.54
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.85
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    1.15
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.26
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:24.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.95e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.81
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.56
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:06.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:06.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.40
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10095.77
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.026
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:48.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5036.40
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:50.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.21
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4025.68
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12055.82
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.54
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000086788

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.37
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999891326

Normal statistic for number of bits   :   -0.86
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:56.37

 All tests were passed




Server wird beendet - Lösche Semaphor 107249692.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:39.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:50.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5554
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:51.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:38.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:37.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:01.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:59.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     335
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:11.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.87
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:42.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.07
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.23
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.18
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.94
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.78
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  388.82
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7102.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.08
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:07.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.67
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.89
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5107.81
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:59.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46141
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870141
  j =  1                              :        399907722
  j =  2                              :            46133
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46028
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870028
  j =  1                              :        399907947
  j =  2                              :            46022
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:29.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:01.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.51e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:38.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.021
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:39.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.75
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.47
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.77
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.58
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.31
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.77
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17238.10
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.45
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.16
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.72
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.59
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.28
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.38
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.34
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.24
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.87
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.35
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.84
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.52
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.17
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.59
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.53
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.35
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.59
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.81
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  449.23
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.16
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5023.19
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.30
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.41
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.81
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.15
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.75
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.05
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.30
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.20
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -1.27
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:24.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.09
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:25.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.93e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.70e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.79
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.21
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.08
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:05.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.02
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10082.30
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9903.11
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:04:15.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5055.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:51.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.78
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:53.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.97
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.27
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11707.21
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.37
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000034135

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.72
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000025453

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:39.15

 All tests were passed




Server wird beendet - Lösche Semaphor 108167196.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5525
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:52.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7083
p-value of test                       :    0.9971


-----------------------------------------------
CPU time used                    :  00:02:38.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:04.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7530
p-value of test                       :  7.0e-3


-----------------------------------------------
CPU time used                    :  00:03:54.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:59.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.43
p-value of test                       :  1.9e-3

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:13.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:44.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.96
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.82
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.13
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.78
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.17
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.84
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:43.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.47
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6993.02
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:42.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.79
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.17
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:04.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.15
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.02
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4999.17
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:54.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45977
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869977
  j =  1                              :        399908047
  j =  2                              :            45975
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45759
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869759
  j =  1                              :        399908487
  j =  2                              :            45749
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:28.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:18.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:59.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:53.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:32.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.94e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.40
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.04
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:47.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.48
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:38.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.57
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.07
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.64
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.67
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.83
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17624.86
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   15.15
p-value of test                       :    0.9991    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.40
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.83
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.09
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.53
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.70
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.36
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.19
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.01
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.54
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.79
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.91
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.83
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.02
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.09
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.15
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.66
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.71
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.89
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.00
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.23
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.77
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5100.89
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.41
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  161.50
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.35
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.45
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4850.48
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.59
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.92
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.34
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :  -0.100
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:25.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.87
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:25.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 6.37e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.85e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.22
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.01
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:04.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.02
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10142.29
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:43.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4791.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:50.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.53
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.55
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11690.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11791.53
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.72
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000048424

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.50
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000038491

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:18.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 H (L=50, r=0)       0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 109248540.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5539
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:52.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7146
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:03.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:04.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:55.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:00.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    3.78
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.33
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:13.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.06
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:42.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.45
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.79
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.18
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.60
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.25
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  270.87
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.24
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6910.04
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:41.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.28
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.38
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:03.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.94
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.44
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:33.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4983.94
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:59.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45803
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869803
  j =  1                              :        399908395
  j =  2                              :            45801
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45840
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869840
  j =  1                              :        399908325
  j =  2                              :            45830
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:27.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.50e-3
p-value of test                       :    0.9961

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:17.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:01.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:54.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:32.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.29e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.053
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:33.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:33.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.80
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.53
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.32
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.57
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.36
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.06
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17625.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.01
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.00
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.11
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.38
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.22
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.28
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.77
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.69
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.57
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.63
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.66
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.04
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.21
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.91
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.89
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.12
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.45
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.33
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.00
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.75
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.87
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.46
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5137.66
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.20
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.56
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  454.78
p-value of test                       :  7.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.29
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4820.09
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.86
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.49
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.60
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.70
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    1.61
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:25.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.60
p-value of test                       :  3.3e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
p-value of test                       :    0.9922

Anderson-Darling statistic = A2       :    5.41
p-value of test                       :  2.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -3.02
p-value of test                       :    0.9987

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 9.94e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.16
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.90
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.50
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:06.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.51
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:04.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.41
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9894.40
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:46.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.90
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.40
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.20
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.09
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11669.61
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.63
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.41
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999920207

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.52
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000060805

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.32

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:13.78

 All tests were passed




Server wird beendet - Lösche Semaphor 110198812.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1267
p-value of test                       :    0.9959

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334387
  j =  1                              :        599997466
  j =  2                              :             1267
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:53.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7520
p-value of test                       :  9.6e-3


-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:55.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:00.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    3.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.06
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    2.40
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:13.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.93
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   20.95
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.51
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.49
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.46
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.87
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.27
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.65
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1348.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:01.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7077.32
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:41.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.26
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:02.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.68
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.04
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5012.15
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:58.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45884
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869884
  j =  1                              :        399908234
  j =  2                              :            45880
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45279
p-value of test                       :    0.9975


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869279
  j =  1                              :        399909446
  j =  2                              :            45271
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:28.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:20.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:03.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:32.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.88e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.62e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.026
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:33.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.56
p-value of test                       :  5.2e-3

-----------------------------------------------
CPU time used                    :  00:01:33.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.49
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.82
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.96
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.03
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:48.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.06
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.16
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:41.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.66
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.99
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.72
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:39.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17490.40
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.11
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.81
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.59
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.10
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.09
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.50
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.48
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.73
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.87
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.54
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.01
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.83
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.23
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.51
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.74
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.04
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.39
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.70
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.95
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.83
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.55
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.72
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.84
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.92
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.54
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.29
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.49
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.06
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.36
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.10
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.71
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.64
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.38
p-value of test                       :  8.7e-3

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.15e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.16e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.28
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.34
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.12
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:06.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10117.52
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10083.80
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.57
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:42.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4961.50
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:47.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.57
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:50.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.87
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4016.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11750.02
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11933.33
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.73
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999983192

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.93
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999979292

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         : 7.74e-3
p-value of test                       :    0.50

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:10.62

 All tests were passed




Server wird beendet - Lösche Semaphor 111181852.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1462
p-value of test                       :  4.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334582
  j =  1                              :        599997076
  j =  2                              :             1462
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:55.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:56.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:00.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    2.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:12.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:42.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.37
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.23
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.31
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.08
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.17
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6945.19
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:42.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.31
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.61
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:03.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.44
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.79
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5105.47
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:59.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45932
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869932
  j =  1                              :        399908137
  j =  2                              :            45930
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45750
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869750
  j =  1                              :        399908505
  j =  2                              :            45740
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:27.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:17.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.88e-3
p-value of test                       :    0.9934

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:54.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:32.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:33.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:34.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.45
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.03
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.70
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.34
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.65
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.85
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.41
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.59
p-value of test                       :  4.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.73
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.94
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17623.24
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.99
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.30
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.25
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.55
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.23
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.46
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.12
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.62
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.62
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.94
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.37
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.67
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.40
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.49
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.14
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.30
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.62
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.84
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.12
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.92
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.30
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.15
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.98
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.43
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  311.27
p-value of test                       :    0.9973


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.34
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.44
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.35
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.18
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.13
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:20.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.36
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :   -1.31
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:22.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.67e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.49
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.96
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:06.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:06.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.82
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9867.19
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:43.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4744.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.01
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.65
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3984.64
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11985.75
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12167.29
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.48
p-value of test                       :    0.9911


-----------------------------------------------
Total number of bits:  7999915080

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.39
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999959639

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   0.042
p-value of test                       :    0.48

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9973

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:34.79

 All tests were passed




Server wird beendet - Lösche Semaphor 112164892.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:50.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5537
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:57.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:41.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7169
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:55.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    2.81
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     556
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:13.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:39.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.54
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.88
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.73
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.39
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.54
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.98
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.37
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.81
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6934.06
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:41.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9907

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.24
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:05.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.20
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.03
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:32.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5188.07
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:54.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46043
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870043
  j =  1                              :        399907918
  j =  2                              :            46035
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45604
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869604
  j =  1                              :        399908793
  j =  2                              :            45602
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:28.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:18.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:44.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:59.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :  5.7e-4    *****

Anderson-Darling statistic = A2       :    6.46
p-value of test                       :  6.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:33.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.64e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.38e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:34.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.42
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.89
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.61
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.47
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.06
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.20
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.30
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.60
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17652.51
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.86
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.10
p-value of test                       :    0.9952


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.22
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.45
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.56
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.48
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.98
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   46.46
p-value of test                       :  3.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.42
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.49
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.93
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.32
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.34
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.66
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.15
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.23
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.90
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.03
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.40
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.85
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.66
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4913.31
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.57
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.25
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.20
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.01
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.73
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.63
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.13
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.64
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.13
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    2.53
p-value of test                       :  5.8e-3



-----------------------------------------------
CPU time used                    :  00:02:24.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9926

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.53e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.94
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.59
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.57
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:06.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.19
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:04.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9969.46
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.89
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:42.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.56
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:50.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.76
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11850.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11749.98
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.21
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000106690

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.62
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000011578

Normal statistic for number of bits   :   0.092
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:51.13
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 51  SampleProd, t = 16              6.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 113049628.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5490
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:55.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:43.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:42.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:59.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4232
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:06.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:58.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:00.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    2.10
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:15.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:42.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   25.92
p-value of test                       :  5.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.50
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.36
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.36
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.92
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.19
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  192.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1409.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:05.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7158.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.22
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.66
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:09.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.44
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.17
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:37.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5131.65
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:58.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46232
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870232
  j =  1                              :        399907542
  j =  2                              :            46220
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45761
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869761
  j =  1                              :        399908481
  j =  2                              :            45755
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 5.74e-3
p-value of test                       :    0.9928

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  7.5e-3

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  9.2e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:29.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:18.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:45.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:03.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:56.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.55e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 2.17e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.21e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.36e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.55
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:41.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:37.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.68
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.77
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.26
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.37
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.57
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.48
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17321.21
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.12
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.77
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.27
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.12
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.14
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.22
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   44.05
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.38
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   35.63
p-value of test                       :  5.1e-3


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.03
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.70
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.43
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.71
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.92
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.12
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.07
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.37
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.28
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.78
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.55
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.03
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.30
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.49
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.23
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.17
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.52
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5023.29
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.50
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.38
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:34.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.54
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:22.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.51
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:22.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   0.033
p-value of test                       :    0.49

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 9.95e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.14e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.02
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.66
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:05.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:05.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9950.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:04:21.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:52.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.02
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:53.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.14
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.17
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11720.77
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:31.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11861.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.97
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000061762

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.39
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000153682

Normal statistic for number of bits   :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.72e-3
p-value of test                       :    0.9951

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:11.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:38.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 26  SimpPoker, r = 0                5.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 113999900.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997399
  j =  2                              :             1299
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5466
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:57.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:43.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:43.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4183
p-value of test                       :    0.9903


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:58.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:07.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:06.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:59.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7501
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:59.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     639
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:12.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.79
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.61
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.39
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.19
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.24
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.91
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.03
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.76
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:08.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7143.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.62
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.86
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:10.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.96
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.29
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5224.44
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:55.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46120
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870120
  j =  1                              :        399907762
  j =  2                              :            46116
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45779
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869779
  j =  1                              :        399908446
  j =  2                              :            45771
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:29.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:19.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:37.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.50e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.03
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.29
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.28
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.14
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.61
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.77
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-3
p-value of test                       :    0.9983

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.28
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.44
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.28
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17367.18
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:52.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.51
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.30
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.88
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.59
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.91
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.09
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.89
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.83
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.89
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.67
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.29
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.78
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.00
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.13
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.07
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.04
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.29
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.30
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.46
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.50
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.19
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.15
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.79
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.99
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.00
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5053.45
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.70
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.80
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.07
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:20.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.60
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :    1.27
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    2.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.83e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.13e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.66
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.43
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.45
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.61
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10048.74
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.060
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:04:13.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.43
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:52.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:53.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4025.35
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.28
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11968.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11867.12
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.37
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999947699

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.29
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000098149

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.053
p-value of test                       :    0.52

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.16
p-value of test                       :    0.9974

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:24.57

 All tests were passed




Server wird beendet - Lösche Semaphor 115048476.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1225
p-value of test                       : 1 -  6.7e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334345
  j =  1                              :        599997550
  j =  2                              :             1225
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5359
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:42.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:57.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:05.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:05.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:55.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:00.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:46.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     268
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:13.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.92
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.81
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.88
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.42
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.20
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.79
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  198.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.41
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1510.58
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6988.24
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:42.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.72
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:05.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.82
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.86
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4928.76
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:58.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45515
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869515
  j =  1                              :        399908975
  j =  2                              :            45505
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45753
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869753
  j =  1                              :        399908498
  j =  2                              :            45745
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:28.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:17.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.6e-3

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:00.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:34.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.83e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 4.55e-4
p-value of test                       :  2.5e-4    *****

Anderson-Darling statistic = A2       :    4.19
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 2.82e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.071
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:34.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.49
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:48.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.44
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.66
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:47.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.56
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.05
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:41.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.28
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.69
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.46e-3
p-value of test                       :    0.9932

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  161.77
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17576.29
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.02
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.24
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.87
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.32
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.46
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.52
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.35
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.36
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.96
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.12
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.58
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.34
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.22
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.44
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.24
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.18
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.48
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.93
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.05
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.55
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.51
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.68
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.15
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.13
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.24
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:22.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.18
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   -1.36
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.85e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 6.51e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.03e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 8.09e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.73
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.98
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.58
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:06.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.07
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:08.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10155.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:38.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4993.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:50.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4003.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4221.44
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11953.33
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11852.27
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.68
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999998132

Normal statistic for number of bits   :  -0.015
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.86
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999932249

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:48.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14          1 -  6.7e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 116129820.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5442
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:56.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4224
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:05.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:06.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:59.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9912

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:13.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    2.66
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.94
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:39.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.24
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.58
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.75
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.09
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.93
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.01
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6886.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:41.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.05
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.02
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:04.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.64
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.64
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:32.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5020.44
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:58.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46090
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870090
  j =  1                              :        399907820
  j =  2                              :            46090
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908185
  j =  2                              :            45900
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:28.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.09e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.68e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:35.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:35.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:48.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.50
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.47
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.52
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.76
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.49
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.35
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.47
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.92
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17533.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.94
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.94
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.54
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.67
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.35
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.41
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.79
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.24
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.47
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.53
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.47
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.43
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.70
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.92
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.78
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  583.23
p-value of test                       :  5.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.28
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.88
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.67
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5155.52
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.43
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.61
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.09
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4891.08
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  320.92
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.99
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.18
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.83
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.81e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.53
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.43
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.53
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:06.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.25
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:08.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.53
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.36
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:38.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.54
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.50
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.61
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.45
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11615.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11597.23
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:29.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.18
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000093604

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.75
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999931730

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:21.20

 All tests were passed




Server wird beendet - Lösche Semaphor 117145628.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1530
p-value of test                       :  5.6e-6    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334650
  j =  1                              :        599996940
  j =  2                              :             1530
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:57.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:42.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:58.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:55.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:01.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    3.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:13.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.02
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.77
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.24
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.75
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.40
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.26
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.36
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.26
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.38
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.30
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6970.86
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.66
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:06.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.45
p-value of test                       :    0.9938


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.55
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:32.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5145.78
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:57.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45937
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869937
  j =  1                              :        399908131
  j =  2                              :            45927
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45470
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869470
  j =  1                              :        399909063
  j =  2                              :            45464
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:27.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:18.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:46.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:35.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.81e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:33.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.43
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.98
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.55
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.48
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.71
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.26
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.51
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.60
p-value of test                       :  2.8e-4    *****

Anderson-Darling statistic = A2       :    4.64
p-value of test                       :  4.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   64.62
p-value of test                       :  8.1e-3

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.60
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.51
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.32
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17530.89
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.47
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.58
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.89
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.50
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.89
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.51
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.76
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.31
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.96
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.16
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.89
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  444.99
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.12
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.98
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.42
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  104.95
p-value of test                       :    0.9958


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.31
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.26
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.06
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.74
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.33
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.24
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.49
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.71
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.51
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.00
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.73
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.88
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.23
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.42
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 9.85e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 6.80e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.64
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.48
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.49
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:04.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:05.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9958.14
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9825.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:42.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.13
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.97
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:51.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.59
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.77
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11521.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.36
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999836801

Normal statistic for number of bits   :   -1.29
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.90
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999949097

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 5.18e-3
p-value of test                       :    0.9946

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.48
p-value of test                       :    0.9934

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:09.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           5.6e-6
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 118161436.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997319
  j =  2                              :             1339
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:56.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:05.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:55.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    2.75
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     839
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.12
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    2.10
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:12.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:42.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.97
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.74
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.22
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.91
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.11
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.81
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.47
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1502.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:02.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7150.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.50
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:04.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.25
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.44
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5222.65
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:53.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45947
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869947
  j =  1                              :        399908111
  j =  2                              :            45937
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45563
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869563
  j =  1                              :        399908878
  j =  2                              :            45555
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:27.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:18.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.78e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.12
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:48.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.00
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.62
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.41
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.40
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.86
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.45
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.13
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.77
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.77
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17468.86
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.38
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.22
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.53
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.47
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.88
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.98
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.04
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.65
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.21
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.18
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.77
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.46
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.98
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.74
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.19
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.69
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.99
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.35
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.60
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.72
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.41
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  438.84
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.92
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.12
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.82
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.78
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.96
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.38
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.67
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    1.65
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:25.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.36
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.29e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.39
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.65
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.20
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:04.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.87
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:06.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.13
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10278.13
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:41.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5073.36
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.87
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.32
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12108.38
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.52
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999992480

Normal statistic for number of bits   :  -0.059
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.78
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000118447

Normal statistic for number of bits   :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   0.078
p-value of test                       :    0.47

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:52.09

 All tests were passed




Server wird beendet - Lösche Semaphor 119144476.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1477
p-value of test                       :  1.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334597
  j =  1                              :        599997046
  j =  2                              :             1477
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5474
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:56.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:42.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:05.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:05.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7027
p-value of test                       :    0.9997    *****


-----------------------------------------------
CPU time used                    :  00:03:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:17.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:48.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.28
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.25
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.67
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.43
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.72
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.16
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.93
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:43.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1494.25
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:01.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7131.90
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:43.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.13
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:05.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.21
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.33
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5116.98
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:59.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45715
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869715
  j =  1                              :        399908572
  j =  2                              :            45711
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45936
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869936
  j =  1                              :        399908128
  j =  2                              :            45936
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:28.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:19.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.13
p-value of test                       :  7.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9963


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:35.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.02e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:33.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:35.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:47.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.77
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.39
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.58
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:47.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.19
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.71
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.99
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.6e-3

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.25
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.24
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17431.38
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.76
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.89
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.79
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.81
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.30
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.97
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.33
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.73
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.64
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.31
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.56
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.10
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.61
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.77
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.35
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.16
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.82
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.77
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.06
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.90
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.11
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4906.16
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.46
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.05
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.62
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.54
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.68
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.91
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.13
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.87
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:25.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.82
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -1.84
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:23.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.05e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.71e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 9.17e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.34
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.85
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.66
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:05.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.50
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:06.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9943.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.57
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.042
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.52
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4990.86
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:50.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3954.96
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3998.02
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11822.72
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11674.93
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.64
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999998693

Normal statistic for number of bits   :  -0.010
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.47
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999846263

Normal statistic for number of bits   :   -1.22
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.97
p-value of test                       :    0.98

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:42.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 20  BirthdaySpacings, t = 16        0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 120094748.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5318
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:56.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:42.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:58.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:05.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:56.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:01.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.70
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    2.69
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:12.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:44.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.76
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.09
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.17
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.67
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.40
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.66
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.21
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.72
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:44.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.69
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7011.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:43.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.34
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:05.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.79
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.85
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:31.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4892.29
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:02.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45908
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869908
  j =  1                              :        399908185
  j =  2                              :            45906
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45902
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869902
  j =  1                              :        399908199
  j =  2                              :            45896
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:27.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  8.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.98
p-value of test                       :  9.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.90e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.55e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:22.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:47.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.27
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.70
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.26
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.74
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.13
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.1e-3

Anderson-Darling statistic = A2       :    3.85
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   63.95
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.66
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.03
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17615.07
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.01
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.92
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.51
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.81
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.72
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.59
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.75
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.08
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.12
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.19
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.94
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.14
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.32
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.24
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.33
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.21
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.92
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.97
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.85
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.32
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:43.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.02
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  319.77
p-value of test                       :    0.9926


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.37
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.98
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.20
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.02
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.94
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.64
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.09
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.48
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.65
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :   -2.77
p-value of test                       :    0.9972



-----------------------------------------------
CPU time used                    :  00:02:23.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.88
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :   -2.05
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 9.67e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.45e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.53
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.09
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:05.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9889.15
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10089.11
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:35.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:44.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.58
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:49.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.36
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4379.91
p-value of test                       :  2.2e-3

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12004.64
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11817.49
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.46
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999990284

Normal statistic for number of bits   :  -0.077
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.17
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999918839

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.85

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.093
p-value of test                       :    0.54

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:12.10

 All tests were passed




Server wird beendet - Lösche Semaphor 121110556.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5411
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:42.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7166
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:35.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:53.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:54.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:01.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:00.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:52.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:57.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    4.01
p-value of test                       :  8.6e-3

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:09.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:35.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.48
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.78
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.26
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.02
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.75
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.48
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.72
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.87
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6993.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:40.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.30
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.44
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:03.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.40
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.65
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4907.85
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:14.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45541
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869541
  j =  1                              :        399908921
  j =  2                              :            45535
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45940
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869940
  j =  1                              :        399908125
  j =  2                              :            45930
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:29.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:45.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:52.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:32.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 4.92e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.71
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:47.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.90
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.15
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:47.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.91
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.20
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.05
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.94
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.48
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.84
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17580.14
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.66
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.01
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.33
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.69
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.81
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.71
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.93
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.87
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.95
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.59
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.86
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.89
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.63
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.10
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.22
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.63
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.55
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.62
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.26
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.81
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.45
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.67
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5134.94
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.16
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.63
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.36
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.39
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5106.65
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.85
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  268.05
p-value of test                       :  9.3e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.69
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   0.025
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:16.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.39
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:20.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 3.48e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.14e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.35
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.18
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:07.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.80
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:08.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10149.54
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:04:04.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:49.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4974.77
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:50.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3900.06
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.60
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.94
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.73
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999963392

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.76
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000144745

Normal statistic for number of bits   :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.87e-3
p-value of test                       :    0.9960

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.29
p-value of test                       :    0.99

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.15

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:27.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 C (L=10000, r=15)   9.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 102531101.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:44.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:37.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:35.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:54.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:01.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:01.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:52.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:58.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    3.20
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:45.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.85
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:10.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:41.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.89
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.12
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.90
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.04
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.48
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.19
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:44.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.07
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:00.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6928.10
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.65
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:03.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.54
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:46.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.46
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4902.81
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:09.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45789
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869789
  j =  1                              :        399908425
  j =  2                              :            45783
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45957
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869957
  j =  1                              :        399908087
  j =  2                              :            45955
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:28.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:18.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:53.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:33.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 7.99e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 7.12e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.45
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:33.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.65
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:48.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.32
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:47.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.82
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.43
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17493.47
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.38
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.52
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.14
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.00
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.79
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.71
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.35
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.72
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.76
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.65
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.46
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.25
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.66
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.93
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.87
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.69
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.43
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.64
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.03
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.31
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.09
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.87
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.63
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.55
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:34.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.31
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.11
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5155.40
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.87
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.96
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:34.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.96
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:17.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.92
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :  -0.024
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:22.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.23
p-value of test                       :    0.99

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.40e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 8.39e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 4.63e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.61
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.93
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.61
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:08.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.14
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:04.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9931.91
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:48.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.43
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.94e-3
p-value of test                       :    0.9937

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.28
p-value of test                       :  6.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5183.27
p-value of test                       :  1.8e-3

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4208.90
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.07
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.49
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:29.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.50
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000025930

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.33
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999996680

Normal statistic for number of bits   :  -0.026
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.17
p-value of test                       :    0.99

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:37.30

 All tests were passed




Server wird beendet - Lösche Semaphor 103120925.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5458
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:46.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:38.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7489
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:36.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:54.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:00.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:01.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:52.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    2.20
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:11.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.53
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:44.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.10
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.00
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.32
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.20
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.48
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  383.84
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.84
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:59.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6835.05
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.50
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:03.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.30
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:46.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.77
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:35.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4940.68
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:02.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45995
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869995
  j =  1                              :        399908013
  j =  2                              :            45989
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46018
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870018
  j =  1                              :        399907966
  j =  2                              :            46014
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:28.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  6.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.45
p-value of test                       :  5.4e-3


-----------------------------------------------
CPU time used                    :  00:02:19.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:45.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:33.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.50e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:35.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:36.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.27
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.86
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.52
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:48.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.19
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   63.86
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.75
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.00
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17331.91
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.43
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.31
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.84
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.20
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.43
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.88
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.03
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.37
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.30
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.31
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.01
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.44
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.37
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.25
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.46
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.55
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.88
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.40
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.72
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.18
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.44
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4798.99
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.81
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.25
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.08
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.48
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4761.00
p-value of test                       :    0.9923


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.27
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.60
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:33.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.12
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:20.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.18
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:24.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.35e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.66
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.11
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:06.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.7e-3

Kolmogorov-Smirnov- statistic = D-    : 6.45e-3
p-value of test                       :    0.9932

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  151.82
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:02:05.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9791.12
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9835.73
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.058
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:43.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4776.35
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4658.90
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.07
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12015.32
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12079.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   85.64
p-value of test                       :  3.9e-3


-----------------------------------------------
Total number of bits:  7999869267

Normal statistic for number of bits   :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.30
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999959357

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:22.75

 All tests were passed




Server wird beendet - Lösche Semaphor 104038429.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5355
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:48.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:46.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4217
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:07.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:22.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:24.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:01.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:35.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.93
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    3.67
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    3.64
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:10.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:40.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.02
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.34
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.36
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.00
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.88
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.60
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:34.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.00
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:30.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.05
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:27.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7157.02
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:38.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.64
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.34
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:03.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.63
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.00
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5235.81
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:56.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45802
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869802
  j =  1                              :        399908398
  j =  2                              :            45798
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46095
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870095
  j =  1                              :        399907814
  j =  2                              :            46087
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:29.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:27.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:56.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:13.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:32.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.58e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.55
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.38
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.19
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.48
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:37.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.29
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.73
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.27
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.11
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17365.01
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.43
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.56
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.14
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.79
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.29
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.90
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.73
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.40
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.32
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.73
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.18
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.28
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.58
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.52
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.10
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.70
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.35
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.01
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.11
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.08
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.82
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.33
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  459.33
p-value of test                       :  4.9e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.48
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4861.46
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.27
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.22
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    1.15
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:23.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.20
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:24.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.23e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 6.55e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.59e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 9.75e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.60
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.33
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.84
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:12.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.62e-3
p-value of test                       :    0.9930

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:13.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9812.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10197.91
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:44.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5029.80
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.29
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:49.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.78
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11758.29
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11537.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:30.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.65
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000031828

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.77
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999936722

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   0.019
p-value of test                       :    0.49

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   0.013
p-value of test                       :    0.49

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         : 6.94e-3
p-value of test                       :    0.50

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:19.45

 All tests were passed




Server wird beendet - Lösche Semaphor 104988701.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5460
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:51.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:38.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:37.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4439
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:54.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7155
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:01.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:02.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:54.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:57.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9934


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    2.42
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    3.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:11.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.65
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    2.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:39.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.09
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.03
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:44.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1497.05
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6912.85
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.75
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:03.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.68
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.49
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:33.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4924.44
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:54.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46218
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870218
  j =  1                              :        399907565
  j =  2                              :            46216
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45925
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869925
  j =  1                              :        399908152
  j =  2                              :            45921
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:28.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:17.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:54.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:33.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 8.21e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.89e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -5.58e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:33.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.35
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.14
p-value of test                       :    0.9925

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.82
p-value of test                       :  8.1e-3

-----------------------------------------------
CPU time used                    :  00:00:47.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.11
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.35
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.79
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.45
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.53
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.3e-3

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17816.33
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.07
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.95
p-value of test                       :    0.9924


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.44
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.38
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.11
p-value of test                       :    0.9924


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.88
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.44
p-value of test                       :    0.9968


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.55
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.32
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.27
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.63
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.09
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.48
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.26
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.17
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.39
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.05
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.92
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.32
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.78
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.14
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.00
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.15
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.37
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.94
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.08
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.66
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.16
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.65
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.63
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:20.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.21
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.40e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 8.82e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.27e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.21
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.16
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:05.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.87
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.29
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.3e-3

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9835.44
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:46.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4979.37
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.27
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.61
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.15
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11370.56
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11822.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:29.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.88
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000067573

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.38
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000094990

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:01.94

 All tests were passed




Server wird beendet - Lösche Semaphor 105840669.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5346
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:56.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:40.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:09.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:11.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:07.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:08.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    3.64
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    3.54
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.19
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:13.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:39.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.44
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   24.50
p-value of test                       :  9.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.55
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.55
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.21
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.16
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.03
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.88
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1533.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:09.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7031.74
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.83
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.50
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.92
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:41.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.45
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:57.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45855
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869855
  j =  1                              :        399908292
  j =  2                              :            45851
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46121
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870121
  j =  1                              :        399907760
  j =  2                              :            46117
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 9.14e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:31.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:21.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:12.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:58.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.45e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 6.23e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.93
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.32
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.46
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.60
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.89
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.99
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:51.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.05
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17277.55
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.80
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.55
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.01
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.58
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.97
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.23
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.48
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.96
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.81
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.74
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.10
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.80
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.90
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.62
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.02
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.35
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.31
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.33
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.77
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.93
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.36
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.01
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.99
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.40
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.86
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.16
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.79
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.70
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.71
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:25.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.25
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   -1.28
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 3.79e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.17e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.33
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.47
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9905

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.95
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:06.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:06.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.38
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.04
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:04:36.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.30
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.59
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4256.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11902.07
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:33.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11677.05
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:35.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.30
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999964034

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.08
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000063463

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :  9.5e-4    *****

Anderson-Darling statistic = A2       :    3.82
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.15
p-value of test                       :    0.02

Sample variance                       :    0.23
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:16.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 27  SimpPoker, r = 27               9.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 106856477.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5539
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:53.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:59.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:10.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:10.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:07.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7480
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:13.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.16
p-value of test                       :    0.9975


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    4.23
p-value of test                       :  6.7e-3

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.26
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:13.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:42.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.02
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.08
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.04
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.52
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.19
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.35
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6950.86
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:57.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.33
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.91
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:15.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.95
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:48.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.85
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5010.47
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:01.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46081
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870081
  j =  1                              :        399907841
  j =  2                              :            46075
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45841
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869841
  j =  1                              :        399908322
  j =  2                              :            45833
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:28.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:24.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:54.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :  1.4e-3

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:08.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:39.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.44e-4
p-value of test                       :  8.8e-3

Kolmogorov-Smirnov- statistic = D-    : 1.84e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:52.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:53.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.04
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.93
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.56
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.84
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.75
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.96
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.24
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.57
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.47
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17178.42
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.46
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.53
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.26
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.58
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.77
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.13
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.59
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.70
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.41
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.39
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.00
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.94
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.76
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.46
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.94
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.96
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.31
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.61
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.44
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.91
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.72
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.38
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.26
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.96
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.04
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.79
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.31
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.58
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.63
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:23.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 8.51e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.92
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.27
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.13
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:31.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.07
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:30.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9859.08
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10065.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.053
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:04:37.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:52.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:54.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.83
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11925.16
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:33.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.33
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000124111

Normal statistic for number of bits   :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.84
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999872339

Normal statistic for number of bits   :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.3e-3

Anderson-Darling statistic = A2       :    4.19
p-value of test                       :  7.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.57
p-value of test                       :  5.2e-3

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    2.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:09.52

 All tests were passed




Server wird beendet - Lösche Semaphor 108298269.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5378
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:53.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:06.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:06.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:57.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:02.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    2.15
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:13.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:45.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.47
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.45
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.33
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.03
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1407.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:01.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7099.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.46
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:06.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.69
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.28
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4973.27
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:53.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45650
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869650
  j =  1                              :        399908702
  j =  2                              :            45646
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45641
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869641
  j =  1                              :        399908723
  j =  2                              :            45631
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:27.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9990    *****


-----------------------------------------------
CPU time used                    :  00:02:16.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:44.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.55e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.01e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.20
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.99
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.64
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   62.95
p-value of test                       :  4.9e-3

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.14
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.05
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:44.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.88
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.52
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17539.72
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.45
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.84
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.74
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.78
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.91
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.37
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.73
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.17
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.67
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.95
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.07
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.20
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.19
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.97
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.13
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.63
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.59
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.33
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.86
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.54
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.48
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.42
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.51
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.42
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.84
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.95
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.71
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.53
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  429.17
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.86
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.18
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:22.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.95
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    1.68
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:22.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.57
p-value of test                       :  7.4e-4    *****

Anderson-Darling statistic = A2       :    4.85
p-value of test                       :  3.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.86
p-value of test                       :  2.1e-3

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.63e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.09e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 8.10e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.66
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.58
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9947.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.62
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.080
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:37.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4745.20
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3936.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4315.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.25
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11995.17
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.09
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000104629

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.65
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999921359

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.80
p-value of test                       :    0.04

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:54.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 47  MaxOft AD, t = 16               0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 109576221.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:49.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:53.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:41.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4464
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:06.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:05.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:57.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:03.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.59
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.16
p-value of test                       :    0.9971

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:14.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.11
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.25
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.31
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.16
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.36
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.38
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.30
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:42.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1528.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6980.07
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:42.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.65
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:06.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.43
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.46
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:33.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.64
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:57.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45923
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869923
  j =  1                              :        399908156
  j =  2                              :            45919
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45949
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869949
  j =  1                              :        399908103
  j =  2                              :            45947
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:27.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:35.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:38.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.39
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.84
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.51
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.40
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.49
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.80
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:41.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17302.76
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.72
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.77
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.71
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.30
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.53
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.38
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.57
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.65
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.48
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.87
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.87
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.65
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.27
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.79
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.94
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.03
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.69
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.67
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.31
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.82
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.81
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.00
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.41
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.62
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.27
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.92
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.50
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.85
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:23.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.85
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:24.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.82e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.86e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.14
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.32
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.54
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:05.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9785.15
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10058.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:37.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5015.42
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:45.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4772.62
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.75
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.04
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.06
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999983891

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.00
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999855182

Normal statistic for number of bits   :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         : 7.16e-3
p-value of test                       :    0.50

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:00.34

 All tests were passed




Server wird beendet - Lösche Semaphor 110526493.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5472
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:54.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:40.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:04.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:04.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:02.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.23
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     334
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.13
p-value of test                       :    0.9994    *****

-----------------------------------------------
CPU time used                    :  00:02:13.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.45
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.85
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.07
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.15
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.57
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.80
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  391.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:01.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7092.20
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:41.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.17
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:04.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.14
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.01
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5136.13
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:57.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45390
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869390
  j =  1                              :        399909224
  j =  2                              :            45382
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46158
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870158
  j =  1                              :        399907691
  j =  2                              :            46144
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:27.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:46.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.7e-3

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.04e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.35e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:35.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.37
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.05
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.67
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.22
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.85
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:41.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.99
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.30
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17710.36
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   60.80
p-value of test                       :  6.0e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.55
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.11
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.39
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.00
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.67
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.01
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.79
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.27
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.23
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.43
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.59
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  179.09
p-value of test                       :  7.8e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.07
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.01
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.13
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.29
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.04
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.32
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.77
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.27
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.79
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.11
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.68
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:34.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.27
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.05
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4904.19
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.15
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.10
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -2.56
p-value of test                       :    0.9947



-----------------------------------------------
CPU time used                    :  00:02:24.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.85
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:23.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
p-value of test                       :    0.9913

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.96
p-value of test                       :    0.02

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.71e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.79e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 9.29e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.91
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.63
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.53
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:04.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.35
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:05.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10343.26
p-value of test                       :  8.1e-3

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10110.80
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:43.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.4e-3

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5109.79
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:49.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.43
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4046.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12029.53
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.07
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.21
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000116875

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.78
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000023983

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.27
p-value of test                       :    0.99

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:55.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP2S, t = 9         0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 111476765.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5422
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:53.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:04.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:02.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.96
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    2.37
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     259
p-value of test                       :    0.9914

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:15.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.16
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    4.15
p-value of test                       :  7.4e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     190
p-value of test                       :  9.3e-4    *****

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:38.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.47
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.78
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.29
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.87
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.55
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.79
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6793.70
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:04.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.53
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.08
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:32.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5142.48
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:58.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45398
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869398
  j =  1                              :        399909207
  j =  2                              :            45392
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45947
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869947
  j =  1                              :        399908106
  j =  2                              :            45947
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:27.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9909

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:45.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:54.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9943

-----------------------------------------------
CPU time used                    :  00:01:35.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 5.56e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.50
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:48.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.27
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.85
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.58
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.02
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.89
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.58
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17380.79
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.92
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.48
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.67
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.62
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.22
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.00
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.80
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.78
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.68
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.50
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.82
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.89
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.65
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.53
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.54
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.70
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   99.35
p-value of test                       :    0.9922


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.82
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.18
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.88
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.82
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.04
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.71
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.24
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.99
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.80
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.82
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.94
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:24.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.03
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:23.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 8.37e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.47e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.10
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.46
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.66
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:04.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.40
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:04.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10285.56
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10141.02
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.01
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.39
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.23
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.01
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11693.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.85
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.90
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999953435

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.21
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999883091

Normal statistic for number of bits   :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:47.34
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs NJumps, t = 16       9.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 112459805.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1250
p-value of test                       :    0.9991    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334370
  j =  1                              :        599997500
  j =  2                              :             1250
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5480
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:53.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:38.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:06.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7521
p-value of test                       :  9.3e-3


-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:00.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     855
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:14.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.47
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    6.06
p-value of test                       :  9.3e-4    *****

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:41.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.81
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.50
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.77
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.43
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:04.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7131.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.93
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:08.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.49
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.72
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4979.22
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:00.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45657
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869657
  j =  1                              :        399908691
  j =  2                              :            45647
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45670
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869670
  j =  1                              :        399908662
  j =  2                              :            45666
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:30.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:18.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:02.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  3.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.99
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.74e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : -8.43e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.52
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.06
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.58
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.40
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.26
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.12
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.84
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.20
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.28
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17321.23
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.37
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.78
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.71
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.47
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.54
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.15
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.77
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.43
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.49
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.99
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.56
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.31
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.39
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.70
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.72
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.59
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.48
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.05
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.94
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.69
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.61
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.51
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.75
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.64
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.80
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.02
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5134.90
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.11
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.34
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.95
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:21.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.76
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-4
p-value of test                       :    0.9940

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.01e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.42
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.48
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.72
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:06.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.61
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:07.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10249.32
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9910.35
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:04:10.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4983.27
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:52.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.41
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.04
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.13
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.47
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000020662

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.89
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000012448

Normal statistic for number of bits   :   0.098
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.014
p-value of test                       :    0.51

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:19.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  3  CollisionOver, t = 2            0.9991 
 25  ClosePairs mNP2, t = 16         9.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 113442845.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:51.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:39.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:04.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:05.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:55.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:01.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    2.17
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:11.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.88
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.09
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   37.48
p-value of test                       :  4.5e-3

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.22
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.75
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.99
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.33
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:01.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6867.80
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:40.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.82
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:03.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.23
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.61
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5003.84
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:56.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46010
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870010
  j =  1                              :        399907983
  j =  2                              :            46004
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46073
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870073
  j =  1                              :        399907855
  j =  2                              :            46071
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:27.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:17.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:00.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:59.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:38.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.31e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 7.59e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.47
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.78
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.82
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   52.25
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:01:42.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.52
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.30
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17509.46
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.79
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.71
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.66
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.51
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.32
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.90
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.05
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.96
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.75
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.74
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.75
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.73
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.79
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.90
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.09
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.46
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.98
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.77
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.20
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.91
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.86
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5092.13
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.80
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.67
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.48
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.81
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.92
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.72
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.95
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.12
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.10
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.043
p-value of test                       :    0.48

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.43e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 5.47e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.37
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.59
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.79
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:05.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.09
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:05.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9852.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.02
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:37.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:47.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.10
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4269.07
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11866.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.11
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.81
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999951086

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.39
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999896669

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:30.88

 All tests were passed




Server wird beendet - Lösche Semaphor 114556957.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5528
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:50.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4239
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:39.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:04.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7105
p-value of test                       :    0.9938


-----------------------------------------------
CPU time used                    :  00:03:04.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:55.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    2.78
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     549
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9957

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:12.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:44.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.40
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.47
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.03
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.92
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1557.87
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6995.12
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:42.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.57
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:46.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.13
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.11
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:02.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46026
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870026
  j =  1                              :        399907951
  j =  2                              :            46020
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46280
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870280
  j =  1                              :        399907443
  j =  2                              :            46274
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:27.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:55.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:33.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 5.42e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.043
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.40
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:01:38.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.05
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:48.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.76
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.70
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:44.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.35
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.30
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.07
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17323.48
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.73
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.08
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.46
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.24
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.71
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.71
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.55
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.83
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.17
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.11
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.20
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.01
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.75
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.79
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.08
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.14
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.48
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.15
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.34
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.99
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.03
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.23
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.80
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.85
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.27
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.99
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.95
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.25
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.45
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.07
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.76
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.36
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -1.61
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:21.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    2.57
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.68e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.90
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.68
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.54
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:05.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:06.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9834.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10142.73
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:39.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5009.15
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.50
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.79
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3867.78
p-value of test                       :    0.9974

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.73
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11919.31
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.35
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000089644

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.93
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999915170

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.83
p-value of test                       :    0.97

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:21.95

 All tests were passed




Server wird beendet - Lösche Semaphor 115474461.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5344
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:52.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:03.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:04.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:55.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:00.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.28
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    2.68
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     845
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.75
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    2.03
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:12.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.19
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.08
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.62
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.06
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.87
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.45
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6948.86
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:40.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.13
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.24
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:04.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.31
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.81
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:33.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5084.95
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:00.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45594
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869594
  j =  1                              :        399908815
  j =  2                              :            45588
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45708
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869708
  j =  1                              :        399908589
  j =  2                              :            45698
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:27.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:19.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:02.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:54.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:33.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.69e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:37.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:37.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.98
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.30
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.20
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.14
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.29
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.33
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.49
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.04
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17352.56
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.81
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.57
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.92
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.53
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.72
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.05
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.09
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.18
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.17
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.04
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.18
p-value of test                       :    0.9918


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.01
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.85
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.99
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.06
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.15
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.04
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.95
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  321.56
p-value of test                       :    0.9910


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4802.55
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.14
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.44
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.24
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.88
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.11
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.02
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.15
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.80
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :   -2.10
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:21.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.35
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :    1.27
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:21.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.11e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.88
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.10
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    5.25
p-value of test                       :  2.3e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  143.30
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:02:04.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.83
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:04.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9820.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:42.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4764.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.60
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:50.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.32
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4284.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11663.97
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11611.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.41
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000085540

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.01
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000094726

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:35.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 88  PeriodsInStrings, r = 0         0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 116424733.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:53.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7515
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:57.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:04.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:05.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:55.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:01.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:14.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:43.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.58
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.35
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.86
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.85
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  380.45
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:46.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1455.61
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7307.27
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.24
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:03.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.33
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.12
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5135.50
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:04.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46031
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870031
  j =  1                              :        399907941
  j =  2                              :            46025
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46052
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870052
  j =  1                              :        399907902
  j =  2                              :            46040
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  5.8e-3

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:27.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:18.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:59.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:33.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.17e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 8.74e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.49e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.30
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.74
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.62
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.29
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.94
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.30
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.52
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17652.05
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.20
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.12
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.23
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.80
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.86
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:39.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.58
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.13
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.57
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.56
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.37
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.92
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.33
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.61
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.52
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.22
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.57
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.70
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.96
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.22
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.04
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.42
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.49
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.85
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  432.87
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.32
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.78
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.65
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5082.43
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.07
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.77
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.06
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -1.49e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:21.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.91
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:21.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.23
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.37
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.18
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.8e-3

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  244.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:06.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10191.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9770.11
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:37.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.63
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4780.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:50.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.11
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11697.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11981.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.41
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000040948

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.93
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999991889

Normal statistic for number of bits   :  -0.064
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.66e-3
p-value of test                       :    0.9906

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:12.73

 All tests were passed




Server wird beendet - Lösche Semaphor 117440541.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  8.6e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  7.3e-3


-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5496
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:54.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7484
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:41.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:58.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:08.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:06.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:00.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:06.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    3.24
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.63
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9924

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    4.86
p-value of test                       :  3.4e-3

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:14.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:40.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.71
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.73
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.41
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.63
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1509.26
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7003.87
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:54.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.26
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.66
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.45
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  161.86
p-value of test                       :  5.5e-3


-----------------------------------------------
CPU time used                    :  00:01:37.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4993.44
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:04.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45870
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869870
  j =  1                              :        399908262
  j =  2                              :            45866
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45645
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869645
  j =  1                              :        399908712
  j =  2                              :            45641
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:30.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:19.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :  1.0e-3

Anderson-Darling statistic = A2       :    4.40
p-value of test                       :  5.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:02.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:37.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.37e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.080
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.60
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.16
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.17
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.47
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.03
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.93
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.83
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.26
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.82
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17377.03
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.17
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.13
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.93
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.03
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.29
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.94
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.93
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.20
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.93
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.04
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.76
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  437.38
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.74
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.07
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.82
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.28
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.63
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.22
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.83
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.86
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.08
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5146.07
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.04
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.62
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.09
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.43
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.66
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  436.77
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.84
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.14
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:21.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.38
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -1.37
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:20.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 5.51e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 5.64e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.69
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.09
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.83
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:04.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.25
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:03.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9726.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.83
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:04:18.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.48
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:53.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.68
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:54.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3932.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11720.34
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:31.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12094.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:32.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.15
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999891575

Normal statistic for number of bits   :   -0.86
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.71
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999966689

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.23
p-value of test                       :    0.01

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:14.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    2.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   0.070
p-value of test                       :    0.47

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:11.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  1  SerialOver, r = 0               8.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 118423581.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.74

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:02.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7500
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:54.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:08.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:13.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:33.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:33.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:33.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:52.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     261
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:14.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.23
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:43.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.60
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.79
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.98
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.07
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:30.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.34
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:08.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7034.79
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:57.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.61
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.55
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:16.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.56
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.24
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5024.85
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:56.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45770
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869770
  j =  1                              :        399908462
  j =  2                              :            45766
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45972
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869972
  j =  1                              :        399908061
  j =  2                              :            45962
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.69e-3
p-value of test                       :    0.9919

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:34.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:26.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:59.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.47e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.65e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.70e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.69e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.88
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:00:24.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:54.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.083
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.15
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.57
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.15
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.02
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:54.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.65
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.27
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17223.74
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.71
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.48
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.39
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.31
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.49
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.58
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.08
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.87
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.27
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.73
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.76
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.32
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.71
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.24
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.15
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.91
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.81
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.55
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.86
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.98
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.49
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.45
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.83
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.81
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.93
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.90
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.30
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4875.17
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.28
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.40
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.22
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:24.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.14
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:24.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :  7.4e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 1.32e-3
p-value of test                       :    0.9987

Anderson-Darling statistic = A2       :    5.98
p-value of test                       :  1.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -3.53
p-value of test                       :    0.9998    *****

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.36e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.37e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.64
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.50
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.47
p-value of test                       :  5.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  145.16
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:02:05.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10156.81
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9927.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:04:30.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4763.24
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:52.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.52
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.56
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11993.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:33.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11609.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:35.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.65
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999864911

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.56
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999902438

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.52e-3
p-value of test                       :    0.9964

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.20
p-value of test                       :    0.99

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:14:48.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 83  LempelZiv, r = 15               0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 119537693.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5483
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:57.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:42.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:43.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:01.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:10.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:09.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:08.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:11.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     950
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    2.48
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.02
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:17.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:42.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.00
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.09
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.23
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.78
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.29
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.89
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.41
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.80
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.07
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:04.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7337.42
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.98
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.01
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:20.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   15.32
p-value of test                       :  9.1e-3


-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.18
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4971.21
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:02.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45716
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869716
  j =  1                              :        399908570
  j =  2                              :            45712
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45930
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869930
  j =  1                              :        399908146
  j =  2                              :            45918
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:33.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:21.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:53.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:09.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:39.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.048
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:24.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.20
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.40
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.73
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.70
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.60
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:52.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.24
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.65
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.37
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17293.32
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.48
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.72
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.58
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.14
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.22
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.10
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.50
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.38
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.62
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.38
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.91
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.07
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.56
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.96
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.44
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.89
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.53
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.30
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.44
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.75
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.29
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.77
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.43
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.49
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  241.56
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.44
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.78
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.59
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.25
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.01
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.54
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -5.96e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.59
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:22.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.91
p-value of test                       :    0.97

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.07e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.10
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.39
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.17
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:03.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.40
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:05.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.65
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.82
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.025
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:04:26.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.25
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.90
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:58.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4203.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4223.46
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:34.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11670.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:35.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.57
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999885665

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.81
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999881219

Normal statistic for number of bits   :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.16
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:57.84

 All tests were passed




Server wird beendet - Lösche Semaphor 120651805.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5241
p-value of test                       :    0.9928


-----------------------------------------------
CPU time used                    :  00:03:53.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:06.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:07.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:01.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:08.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:50.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    2.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:14.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:44.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.67
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.05
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.60
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.95
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.67
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.92
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:03.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7066.33
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:09.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.06
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.47
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:37.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4927.43
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:03.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45650
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869650
  j =  1                              :        399908705
  j =  2                              :            45640
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45893
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869893
  j =  1                              :        399908217
  j =  2                              :            45887
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:28.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:16.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:52.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.39e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.74e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.12e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.44e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:47.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.07
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.46
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.33
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.78
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.14
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17219.76
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.59
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.13
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.56
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.06
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.54
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.26
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.66
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.71
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.86
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.93
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.77
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.07
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.38
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.54
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.23
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.98
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.05
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.59
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.38
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.12
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.86
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.97
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.16
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.82
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.67
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.89
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4907.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.87
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.73
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:31.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.54
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:10.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.70
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :  -0.010
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:10.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 3.17e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.57e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:40.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.42
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.75
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:52.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:53.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9756.62
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10275.29
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.059
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:19.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.11
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:41.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.39
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:41.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.32
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.62
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.98
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.31
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.28
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000102019

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.58
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000009007

Normal statistic for number of bits   :   0.071
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:58:27.38

 All tests were passed




Server wird beendet - Lösche Semaphor 121798685.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:48.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1263
p-value of test                       :    0.9971

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334383
  j =  1                              :        599997474
  j =  2                              :             1263
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5427
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:41.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:34.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4190
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:53.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:02.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:02.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:56.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    2.77
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     852
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.02
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9950

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9922

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:36.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.00
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.46
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.54
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  287.37
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.67
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1406.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:05.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7067.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.92
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:11.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.75
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4969.87
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:58.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46097
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870097
  j =  1                              :        399907811
  j =  2                              :            46087
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45952
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869952
  j =  1                              :        399908101
  j =  2                              :            45942
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:30.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:18.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:53.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.45e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.42
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.023
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:43.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.60
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.55
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.79
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.07
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.20
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.71
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.48
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17490.89
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.69
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.24
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.55
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.63
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.37
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.99
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.92
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.10
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.52
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.03
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  203.88
p-value of test                       :  1.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.88
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.43
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.02
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.18
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.93
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.57
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.26
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.58
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.82
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.25
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.36
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.85
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.61
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.67
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.42
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.73
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.03
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.62
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:26.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.83
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:26.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    2.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.93e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 5.15e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.94
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.16
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:08.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.70
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:08.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.39
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.98
p-value of test                       :  9.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10389.89
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:04:21.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.05
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:53.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.74
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:54.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.71
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.21
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:36.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11924.79
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:34.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.46
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000035434

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.73
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999876761

Normal statistic for number of bits   :   -0.97
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9952

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:16:11.38

 All tests were passed




Server wird beendet - Lösche Semaphor 102563870.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5522
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:47.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:37.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7495
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:37.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:54.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4477
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:02.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:52.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:58.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.22
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.15
p-value of test                       :    0.9985

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:12.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    2.13
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:38.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.61
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.13
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.55
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.11
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.46
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.45
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.46
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.31
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  472.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.42
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:59.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7115.01
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.18
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.85
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.26
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5001.33
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:53.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45553
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869553
  j =  1                              :        399908901
  j =  2                              :            45539
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46150
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870150
  j =  1                              :        399907706
  j =  2                              :            46138
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:27.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:16.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:43.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 9.18e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:00.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 9.77e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.065
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:34.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.41
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:47.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.60
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.51
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.76
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 9.97e-4
p-value of test                       :    0.9990

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.82
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.42
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.51
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.65
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.16
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17364.67
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.86
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.32
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   47.72
p-value of test                       :  4.0e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.49
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.14
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.39
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.88
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.36
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.00
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.43
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.34
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.86
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.80
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.55
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.62
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.05
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.84
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.12
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.77
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.26
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.72
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.62
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.26
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.20
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.93
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.51
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4900.04
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.09
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.30
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.32
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   0.066
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:26.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.10
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :    1.77
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:27.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.94
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.06
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.57
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:08.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.30
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:08.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10152.94
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.96
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:46.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.78
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4755.08
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.05
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.87
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11911.95
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11568.93
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.70
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  8000056461

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.76
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999853874

Normal statistic for number of bits   :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.81
p-value of test                       :    0.04

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:37.51

 All tests were passed




Server wird beendet - Lösche Semaphor 103317534.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:48.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:36.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4446
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:02.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:02.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:52.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:00.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    2.09
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:12.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.77
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:42.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.27
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.39
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.38
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.24
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.70
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.83
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.43
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.03
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:58.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7105.13
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:42.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.65
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:03.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.27
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.60
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5097.69
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:57.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46027
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870027
  j =  1                              :        399907947
  j =  2                              :            46025
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45822
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869822
  j =  1                              :        399908362
  j =  2                              :            45810
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:27.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:27.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:17.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:44.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:59.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:54.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:32.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:31.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:31.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.98
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.66
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.12
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.70
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.07
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.31
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17550.21
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.65
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.79
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.98
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.85
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.53
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.16
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.79
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.99
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.64
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.45
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.54
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.06
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.84
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.13
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.61
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.53
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.37
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  175.99
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.77
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.16
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.62
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.31
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.90
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.89
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.60
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.05
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.38
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.76
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.99
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.92
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:25.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.58
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -1.72
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:26.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    0.20
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.59e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.50e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.39
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.30
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.18
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:08.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.70
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:08.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10203.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.26
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:41.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.18
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:50.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.26
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.35
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11847.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11646.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.28
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000036184

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.77
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999868679

Normal statistic for number of bits   :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.92

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:19.79

 All tests were passed




Server wird beendet - Lösche Semaphor 104202270.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5405
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:47.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:38.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:36.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:53.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:02.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:01.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:51.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:57.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.41
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:12.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.05
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.72
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.74
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.77
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1359.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:04.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7017.74
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.85
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.67
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:06.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.12
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.81
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:35.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4941.02
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:52.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46175
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870175
  j =  1                              :        399907652
  j =  2                              :            46171
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45826
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869826
  j =  1                              :        399908349
  j =  2                              :            45824
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:28.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:19.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:00.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.07e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.41e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:38.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.56
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.63
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:48.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.41
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.03
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.28
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.96
p-value of test                       :  9.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   89.97
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17334.80
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.08
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.97
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.86
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.54
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.77
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.05
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.85
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.66
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.64
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.35
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.75
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  420.25
p-value of test                       :    0.9960


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.16
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.07
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.74
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.12
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.45
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.56
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.47
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.70
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.78
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.44
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.05
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.65
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.49
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.27
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  436.55
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.82
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.62
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:22.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.97
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.71e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.14e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 6.61e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.81
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.27
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.63
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.06
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10050.68
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10084.48
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:04:10.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4958.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:51.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.25
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11682.38
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:29.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11673.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.40
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999952823

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.82
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999948266

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.099
p-value of test                       :    0.46

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:26.60

 All tests were passed




Server wird beendet - Lösche Semaphor 105119774.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1256
p-value of test                       :    0.9984

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334376
  j =  1                              :        599997488
  j =  2                              :             1256
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5464
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:48.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:38.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:37.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:01.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:01.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:51.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:58.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:14.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:42.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.78
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.61
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.13
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.59
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.20
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:43.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1499.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:03.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7198.84
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.01
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:02.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.18
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.77
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:35.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.38
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:55.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45491
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869491
  j =  1                              :        399909021
  j =  2                              :            45485
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45869
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869869
  j =  1                              :        399908270
  j =  2                              :            45853
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:28.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:19.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:55.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:33.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 8.63e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.25
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.94
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:47.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.21
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.41
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.83
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.07
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.51
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.15
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.85
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 7.11e-3
p-value of test                       :    0.9924

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   92.38
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17795.54
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.11
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.68
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.42
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.39
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.52
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.33
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.34
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.84
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.74
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.11
p-value of test                       :  9.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.60
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.02
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.72
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.35
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.38
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.34
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.16
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.66
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.99
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.22
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.92
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.43
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.90
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.26
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5166.60
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.29
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.52
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:34.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.05
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :  -0.069
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.77
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 8.74e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.91e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 9.33e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.40
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.85
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.27
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.05
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:07.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10088.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10145.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:04:03.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4731.09
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.07
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:52.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.81
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.30
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11889.54
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11725.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.54
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000039268

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.98
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000134017

Normal statistic for number of bits   :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.09

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:35.29

 All tests were passed




Server wird beendet - Lösche Semaphor 106168350.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1251
p-value of test                       :    0.9990    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334371
  j =  1                              :        599997498
  j =  2                              :             1251
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:49.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7117
p-value of test                       :    0.9908


-----------------------------------------------
CPU time used                    :  00:03:02.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:01.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:53.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:00.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.25
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    5.44
p-value of test                       :  1.8e-3

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     640
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.57
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:13.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.83
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.96
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.28
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.13
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.09
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.83
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.08
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  473.19
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6965.24
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:40.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.57
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.59
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   88.12
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:02.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.15
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.67
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:33.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5024.86
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:53.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45705
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869705
  j =  1                              :        399908593
  j =  2                              :            45699
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45862
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869862
  j =  1                              :        399908280
  j =  2                              :            45854
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:27.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:17.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:54.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 9.25e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:31.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:47.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.70
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.74
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.24
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:38.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.01
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.92
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17510.58
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.92
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.57
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.57
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.21
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.06
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.96
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.39
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.47
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.14
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.14
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.67
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.68
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.67
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.16
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.47
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.02
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.37
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.07
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  110.32
p-value of test                       :  4.0e-3


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.08
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.84
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5115.79
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.29
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.75
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.46
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.19
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.98
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.15
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  160.37
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.20
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    1.27
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:23.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.55
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:24.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.69
p-value of test                       :    0.05

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.29e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.21
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.28
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.93
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:05.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.21
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:08.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9909.21
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10090.49
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:40.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4983.13
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5005.64
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.89
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.32
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11603.93
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11687.45
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.54
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999984278

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.37
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999981944

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:20.78
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 107184158.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1470
p-value of test                       :  2.4e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334590
  j =  1                              :        599997060
  j =  2                              :             1470
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5496
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:49.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:39.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:38.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:02.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7574
p-value of test                       :  1.5e-3


-----------------------------------------------
CPU time used                    :  00:03:02.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:53.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:00.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.99
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    2.84
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     337
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:11.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:43.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.22
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.31
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.70
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.85
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.03
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.99
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.94
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.97
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.11
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:59.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6986.86
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.95
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.03e-3
p-value of test                       :    0.9914

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   84.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:07.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.13
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.76
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5134.62
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:57.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46270
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870270
  j =  1                              :        399907460
  j =  2                              :            46270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45839
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869839
  j =  1                              :        399908322
  j =  2                              :            45839
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:27.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:17.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9938

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9952


-----------------------------------------------
CPU time used                    :  00:01:58.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:32.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.45e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.37e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:34.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.89
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.26
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.59
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.43
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.29
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.68
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.66
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.18
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.93
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17454.70
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.07
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.09
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.07
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.50
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.62
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.99
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.21
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.95
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.64
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.88
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.75
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.00
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.90
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.03
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.72
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.70
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.20
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.95
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.53
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.48
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.53
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.40
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.76
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.79
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.37
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.61
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.35
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.65
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:21.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.13
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :  -0.082
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:20.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.81e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 4.80e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   25.53
p-value of test                       :  1.3e-3

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.50
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.05
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:05.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.16
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:05.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:41.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.22
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.62
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:49.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4014.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.22
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.39
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11834.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.19
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999882863

Normal statistic for number of bits   :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.99
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000081940

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.56e-3
p-value of test                       :    0.9908

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.28
p-value of test                       :    0.99

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:04.12

 All tests were passed




Server wird beendet - Lösche Semaphor 108036126.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:50.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4210
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:39.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:38.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:04.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:54.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7473
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:00.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:46.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    2.22
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.32
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:06.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.09
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    4.29
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:02:33.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.50
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    5.71
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.58
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.99
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.73
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:45.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.45
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:58.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6907.84
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:41.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.98
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:04.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.10
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.38
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5115.74
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:50.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46067
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870067
  j =  1                              :        399907867
  j =  2                              :            46065
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45857
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869857
  j =  1                              :        399908290
  j =  2                              :            45849
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  1.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:28.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:17.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.55e-3
p-value of test                       :    0.9938

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:32.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.18e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:32.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.23
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:47.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.05
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:37.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.32
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.53
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17357.91
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.90
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.92
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.91
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.94
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.75
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.47
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.36
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.88
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.38
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.76
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.43
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.21
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.40
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.68
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.66
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.76
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.16
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.18
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.39
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4844.97
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.57
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.09
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.44
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.36
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.23
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.68
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.61
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:24.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.59
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :    1.38
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:24.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 4.73e-3
p-value of test                       :    0.9951

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.86
p-value of test                       :    0.97

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.84e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.76
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.80
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:04.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.61
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:06.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10187.76
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10146.56
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:39.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4770.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4801.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.92
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4196.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12012.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.42
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.95
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000105334

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.68
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000116323

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.19
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:25.89

 All tests were passed




Server wird beendet - Lösche Semaphor 108953630.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5292
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:53.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:38.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:04.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:55.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:59.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:44.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:12.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.77
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:40.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.35
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.87
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.67
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.61
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.37
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.13
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:59.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7184.03
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.30
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:04.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.38
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.23
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:33.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5113.02
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:52.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45842
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869842
  j =  1                              :        399908319
  j =  2                              :            45836
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45775
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869775
  j =  1                              :        399908453
  j =  2                              :            45769
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 8.45e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:28.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  4.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.04
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.92e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 8.06e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:26.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.90
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.82
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:48.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.73
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:47.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.16
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.98
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:03.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.49
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.53
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.65
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  100.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17140.66
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.34
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.07
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.44
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.95
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.92
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.70
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.23
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.61
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.67
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.69
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.52
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.39
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.60
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.62
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.82
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.89
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.94
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.81
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.59
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.98
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.90
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.09
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.84
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.38
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.08
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.29
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.90
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.46
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.50
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.46
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.49
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.39
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:24.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.91
p-value of test                       :    0.97

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.00e-2
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.03
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.63
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.97
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:04.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.29
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9964.95
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9834.85
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.81
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:03:42.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.96
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.01
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.25
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4241.85
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11781.08
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11969.93
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.87
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999944225

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.10
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000077140

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-3
p-value of test                       :    0.9986

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.76
p-value of test                       :    0.04

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:55.98

 All tests were passed




Server wird beendet - Lösche Semaphor 109903902.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5467
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:56.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:39.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4226
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:04.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:04.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:55.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:59.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.94
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    2.01
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:12.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:42.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.86
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.29
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.56
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.12
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.55
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.00
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7106.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.41
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.03
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:04.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.00
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  147.98
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5009.85
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:56.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45751
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869751
  j =  1                              :        399908501
  j =  2                              :            45745
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45777
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869777
  j =  1                              :        399908447
  j =  2                              :            45775
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:28.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:18.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:46.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 8.44e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.31e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:34.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:34.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:47.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.51
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.93
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:47.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.33
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.55
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.97
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-3
p-value of test                       :    0.9981

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  161.38
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17610.33
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.10
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.82
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.83
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.06
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.96
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.43
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.05
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.63
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.53
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.26
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.80
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.04
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.76
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.69
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.13
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.48
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  568.48
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.14
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.27
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.54
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.56
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.75
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.02
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.11
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.95
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.39
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.83
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.19
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.16
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.79
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    1.55
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:23.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.58
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:23.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.26
p-value of test                       :    0.99

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.03e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.46
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.84
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.33
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:04.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.61
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:05.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9987.13
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9914.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:42.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.71
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5021.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.02
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3929.68
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11729.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.94
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000100858

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.65
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  8000114976

Normal statistic for number of bits   :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.12

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:37.28

 All tests were passed




Server wird beendet - Lösche Semaphor 110886942.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1477
p-value of test                       :  1.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334597
  j =  1                              :        599997046
  j =  2                              :             1477
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5530
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:59.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:04.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:55.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:59.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     952
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    3.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.76
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    3.37
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    2.32
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:12.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:39.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   25.70
p-value of test                       :  5.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.07
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.80
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.71
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.26
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  172.73
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.64
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:44.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1365.89
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:00.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7119.11
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.67
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:05.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.16
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.44
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:33.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5156.07
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:55.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45745
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869745
  j =  1                              :        399908514
  j =  2                              :            45737
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45903
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869903
  j =  1                              :        399908194
  j =  2                              :            45903
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:27.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:17.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:59.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.33e-3
p-value of test                       :    0.9976

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:32.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:35.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.58
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:47.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.03
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:47.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.30
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:37.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.48
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 9.02e-3
p-value of test                       :    0.9902

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.19
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.27
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.20
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9972

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17440.96
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.07
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.76
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.09
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.34
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   15.55
p-value of test                       :    0.9988


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.96
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.97
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.34
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.86
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.94
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.00
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  566.22
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.58
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.94
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.45
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.88
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.53
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.13
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.26
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.56
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4900.44
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  283.92
p-value of test                       : 1 -  9.6e-5    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.54
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:34.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.70
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.89
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.44
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.54
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.78
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.94
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:22.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.80
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -1.43
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:21.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.64e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.35e-4
p-value of test                       :    0.9922

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.25
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.48
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:03.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.28
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9758.68
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.60
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:43.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.17
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:49.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.12
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.95
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3982.04
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11590.95
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.29
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.16
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000081226

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.46
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000033769

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.07e-3
p-value of test                       :    0.9925

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.028
p-value of test                       :    0.51

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:27.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 27  SimpPoker, r = 27               5.7e-4
 78  RandomWalk1 R (L=10000, r=0)   1 -  9.6e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 111869982.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:55.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:42.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:05.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:05.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:56.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:00.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    4.68
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.87
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:12.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:37.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.03
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.67
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.13
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.06
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.73
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.54
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.40
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:00.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7002.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.30
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.34
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:05.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.62
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.82
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:33.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.52
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:54.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45765
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869765
  j =  1                              :        399908474
  j =  2                              :            45757
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45599
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869599
  j =  1                              :        399908808
  j =  2                              :            45587
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:26.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:17.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:46.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:01.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:54.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:33.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.58e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.42
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.18
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.50
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:47.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.78
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.43
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.34
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:36.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.91
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.53
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17645.03
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.23
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.33
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.36
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.76
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.42
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.77
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.58
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.71
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.52
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.90
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.56
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  574.22
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.84
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.57
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.09
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.69
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.80
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.71
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.37
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.36
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.72
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5112.45
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.43
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  147.57
p-value of test                       :    0.9979


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.32
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.19
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.27
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.34
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.50
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.57
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:22.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.17
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -1.31
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.5e-3

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.17e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.96e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.32
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.82
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  243.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:02.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.27
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.24
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4719.49
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.99
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:51.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.75
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.34
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.69
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11628.73
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.92
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999962306

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.65
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999931322

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   0.015
p-value of test                       :    0.49

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.18
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   0.063
p-value of test                       :    0.48

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:42.17

 All tests were passed




Server wird beendet - Lösche Semaphor 112853022.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:57.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:05.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:05.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:55.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:00.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     844
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:11.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    2.20
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.48
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.10
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.56
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.60
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.25
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.29
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.42
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.72
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:45.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:00.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6838.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:06.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.11
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.95
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:32.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5146.35
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:55.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45958
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869958
  j =  1                              :        399908087
  j =  2                              :            45952
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46005
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870005
  j =  1                              :        399907993
  j =  2                              :            45999
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:26.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:18.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:53.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 7.97e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 8.88e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:33.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:35.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.29
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:47.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.41
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.13
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:36.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.83
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17518.36
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.91
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.91
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.52
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.23
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.14
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.49
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.18
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.39
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.18
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.78
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.32
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.77
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.06
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.53
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.69
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.87
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.50
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.25
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.33
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.35
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.11
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.30
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.61
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.60
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.38
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4861.10
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.38
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.40
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:34.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.14
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.57
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:22.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.90
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.08
p-value of test                       :    0.98

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.24e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.51e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.74
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.14
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.93
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:05.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:03.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9744.61
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.43
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:37.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.35
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4781.23
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.44
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11984.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12119.50
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.84
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000061120

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.57
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000100612

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:39.32

 All tests were passed




Server wird beendet - Lösche Semaphor 113868830.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:57.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4211
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:58.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:07.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:05.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7135
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:56.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:04:01.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.05
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    2.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     272
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:14.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:40.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.16
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.33
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.88
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.45
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  197.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.08
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.62
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:00.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7003.49
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:44.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:05.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.19
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5037.51
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:55.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46103
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870103
  j =  1                              :        399907797
  j =  2                              :            46097
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46249
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870249
  j =  1                              :        399907503
  j =  2                              :            46247
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:25.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:17.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:44.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:01.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  2.6e-3

Anderson-Darling statistic = A2       :    4.09
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:01:54.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:32.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.67e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.41e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.041
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:33.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:34.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.56
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:47.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.80
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:47.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.00
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.50
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.65
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.86
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.85
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.85
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.96e-3
p-value of test                       :    0.9926

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.88
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17366.54
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.20
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.96
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.60
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.82
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.55
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.14
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.47
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.54
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.00
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.73
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.12
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.88
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.37
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.89
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.55
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.65
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.88
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.49
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.41
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.50
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.75
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.30
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.93
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.13
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  445.78
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.19
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.30
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.24
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.88
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :    2.48
p-value of test                       :  6.5e-3



-----------------------------------------------
CPU time used                    :  00:02:22.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   35.69
p-value of test                       :  3.6e-4    *****


-----------------------------------------------
Normal statistic for number of jumps  :   -3.77
p-value of test                       : 1 -  8.3e-5    *****



-----------------------------------------------
CPU time used                    :  00:02:23.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.23
p-value of test                       :    0.99

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.39e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.74e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.21
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.88
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.66
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.86
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:05.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.32
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:37.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.00
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4980.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.83
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.82
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11844.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11557.22
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:29.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.87
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000151192

Normal statistic for number of bits   :    1.20
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.00
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999899378

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:08.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 81  LinearComp, r = 29             1 -  8.3e-5
 81  LinearComp, r = 0               3.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 114884638.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1265
p-value of test                       :    0.9966

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334385
  j =  1                              :        599997470
  j =  2                              :             1265
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:58.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:43.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:41.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4445
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:58.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:07.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:06.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:56.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:01.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    2.46
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.97
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:13.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:40.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.92
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.03
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.08
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.84
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1368.62
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7017.64
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.94
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.83
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:02.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.26
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.29
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:32.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4992.95
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:55.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908182
  j =  2                              :            45906
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45506
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869506
  j =  1                              :        399908993
  j =  2                              :            45496
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:25.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:16.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:53.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:32.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.79e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 2.28e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.58e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.81
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:47.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.76
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.63
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.77
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.42
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.63
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.42
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16977.62
p-value of test                       :    0.9927



-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.41
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.95
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.87
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.68
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.24
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.63
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.84
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.97
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.49
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.96
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.48
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.97
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.17
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.82
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.64
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.99
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  566.81
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.10
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.00
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.51
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.11
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4783.22
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.64
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.56
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.66
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.63
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5076.20
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.29
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.31
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:34.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.00
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:21.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.38
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:22.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.31e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.94
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.17
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.59
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:04.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.91
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:04.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9685.58
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.45
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.042
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:40.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.30
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.50
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:50.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.39
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11748.22
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11687.31
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.58
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000051958

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.74
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000076894

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.19e-3
p-value of test                       :    0.9988

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.023
p-value of test                       :    0.51

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.1e-3

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:34.47

 All tests were passed




Server wird beendet - Lösche Semaphor 115867678.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5299
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:56.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:43.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:08.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:05.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:56.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:02.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.63
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:13.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:42.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.14
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.62
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.66
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.85
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  197.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.37
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:44.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:59.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7129.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:43.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.34
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.07
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:03.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.64
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.55
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:33.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4979.72
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:55.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45811
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869811
  j =  1                              :        399908379
  j =  2                              :            45809
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46020
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870020
  j =  1                              :        399907963
  j =  2                              :            46014
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:25.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:17.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:45.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.03e-3
p-value of test                       :    0.9920

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:59.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:53.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.88e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.01e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.023
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:34.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.13
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.82
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.99
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.18
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.39
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:36.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9936

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.48
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.15
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17409.31
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.69
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.81
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.76
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.16
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.41
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.35
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.81
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.14
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.54
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.98
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.53
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.62
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.65
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.29
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.05
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.32
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.79
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.10
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.11
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.49
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.45
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4913.80
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.88
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.54
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.56
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.40
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4859.02
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.70
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.81
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.45
p-value of test                       :    0.9914


-----------------------------------------------
Normal statistic for number of jumps  :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:20.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.84
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:22.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.16
p-value of test                       :    0.9976

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.09e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.60
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.11
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.15
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:06.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10181.89
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9878.56
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:38.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5033.64
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.98
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.54
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.72
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11974.65
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11621.77
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.99
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000004495

Normal statistic for number of bits   :   0.036
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.00
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999853043

Normal statistic for number of bits   :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.17
p-value of test                       :    0.98

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.23
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.0e-3

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.37
p-value of test                       :  8.9e-3

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.19
p-value of test                       :    0.9951

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:59.52

 All tests were passed




Server wird beendet - Lösche Semaphor 116883486.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:49.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5532
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:57.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:43.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:08.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:08.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:57.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:02.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    2.75
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     843
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9920

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:14.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:44.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.25
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   22.20
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.18
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.65
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.25
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.98
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7092.71
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.43
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.90
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:02.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.45
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.38
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:32.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5143.45
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:55.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45948
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869948
  j =  1                              :        399908109
  j =  2                              :            45938
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46292
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870292
  j =  1                              :        399907417
  j =  2                              :            46290
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:26.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:16.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:59.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:53.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.33e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:47.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.20
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.90
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.72
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.28
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.44
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:37.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.6e-3

Kolmogorov-Smirnov- statistic = D-    : 8.04e-3
p-value of test                       :    0.9914

Anderson-Darling statistic = A2       :    5.60
p-value of test                       :  1.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   82.31
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17286.91
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.21
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.59
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.46
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.29
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.90
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.72
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.99
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.54
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.96
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.34
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.85
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.97
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.19
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.48
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.25
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.28
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.47
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.54
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.09
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.02
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.27
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5076.64
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.83
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.79
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.42
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.78
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.03
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.69
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.75
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:21.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.10
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :   -1.40
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:22.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.74e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.58e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.22
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.68
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:04.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.79
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:05.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9913.56
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.83
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:39.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.49
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:50.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.04
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.27
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11807.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11923.96
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.15
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999972668

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.08
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000025240

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:50.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 72  Savir2                          0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 117866526.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:53.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:56.84

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:42.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4138
p-value of test                       :    0.9988


-----------------------------------------------
CPU time used                    :  00:01:58.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:08.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:05.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:56.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:01.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.08
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.57
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     551
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    2.16
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     259
p-value of test                       :    0.9914

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:15.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:41.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.31
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.00
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   39.03
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.31
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.24
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.75
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  174.75
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:43.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1337.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:01.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6924.93
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:43.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.36
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:02.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.11
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.78
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:32.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5134.10
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:52.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46090
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870090
  j =  1                              :        399907825
  j =  2                              :            46080
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869892
  j =  1                              :        399908221
  j =  2                              :            45882
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:27.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:16.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:58.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:33.48

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.53e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:32.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.054
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:32.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.95
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:48.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.86
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:37.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.90
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.74
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.24
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17418.30
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.91
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.29
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.30
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.56
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.62
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.50
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.43
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.94
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.29
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.45
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.36
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.02
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.48
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.65
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.28
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.61
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.48
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.45
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.58
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.93
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.67
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.09
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.05
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.28
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.87
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.36
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5186.73
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.74
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.14
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.46
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -1.21
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:21.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.04
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:22.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 6.12e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.75e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 9.71e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.79
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.82
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.26
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:04.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9863.69
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:40.20

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.26
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.20
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.82
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.64
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11983.22
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.70
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000083539

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.47
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000147637

Normal statistic for number of bits   :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.19
p-value of test                       :    0.9957

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:06.35

 All tests were passed




Server wird beendet - Lösche Semaphor 118849566.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5434
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:54.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:59.01

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:06.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:05.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:57.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:02.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.86
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    4.11
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:15.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:44.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.05
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.49
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.95
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.68
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.25
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.55
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.70
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:59.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6781.34
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:43.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.12
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.92
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:03.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.04
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.64
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:32.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5109.34
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:55.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46159
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870159
  j =  1                              :        399907688
  j =  2                              :            46147
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46068
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870068
  j =  1                              :        399907868
  j =  2                              :            46060
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.59

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:26.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:16.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  4.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:53.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:01:32.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 8.99e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.91e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 3.09e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:32.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:31.23

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.19
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.80
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.82
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:00:47.82

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.91
p-value of test                       :  1.0e-2

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.18
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.54
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:37.19

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.47
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.50
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17301.94
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.84
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.57
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.58
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.83
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.82
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.32
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.55
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.80
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.24
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.60
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.67
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.85
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.22
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.16
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.89
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.61
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.81
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.88
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.48
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.80
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.16
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.68
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.17
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.95
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:34.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.39
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.98
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5115.46
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.37
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.42
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.27
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:20.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.39
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:21.44

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.66e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 8.33e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.44e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.00
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.15
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.4e-3

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    3.85
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:04.28

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.27e-3
p-value of test                       :    0.9922

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.4e-3

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  250.72
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:02:05.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10095.38
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9937.06
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:38.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4786.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.66e-3
p-value of test                       :    0.9951

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4643.39
p-value of test                       :    0.9943

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.94
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4259.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.20
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11764.00
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.78
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999906134

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.42
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000042898

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:44.68

 All tests were passed




Server wird beendet - Lösche Semaphor 119898142.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.30

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5461
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:55.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4470
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7518
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7477
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:07.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:06.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:57.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:02.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.29
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:14.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:44.61

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.24
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.17
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.83
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.11
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.76
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.49
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.52
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  370.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:43.89

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1381.89
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:00.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6975.28
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   84.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:03.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.57
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.90
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:32.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5161.45
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:54.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45674
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869674
  j =  1                              :        399908656
  j =  2                              :            45666
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45990
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869990
  j =  1                              :        399908021
  j =  2                              :            45988
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:26.92

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:17.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:44.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:59.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:54.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.63e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.34

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:32.98

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.01
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.91
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.17
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.57
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.90
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.74
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.70
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-3
p-value of test                       :    0.9985

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   68.27
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 8.18e-3
p-value of test                       :    0.9912

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   95.15
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17352.73
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.74
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.25
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.04
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.11
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.39
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.13
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.99
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.65
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.30
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.80
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.76
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.87
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.53
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.45
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.86
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.11
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.15
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.32
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.98
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.50
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.01
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.98
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5113.76
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.24
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.47
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.24
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.05
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.01
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  317.33
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.98
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.07
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:21.90

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.96
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:21.27

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.80
p-value of test                       :    0.04

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.02e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 6.13e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.53e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.36
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.87
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.07
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:03.45

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:03.97

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9987.18
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:38.95

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.56
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.55
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:49.87

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.50
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11729.65
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12054.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.56
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000003064

Normal statistic for number of bits   :   0.024
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.97
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000038143

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.96
p-value of test                       :    0.02

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n91, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   0.044
p-value of test                       :    0.48

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:59.73

 All tests were passed




Server wird beendet - Lösche Semaphor 120913950.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5575
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:41.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:35.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7504
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:33.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:53.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:59.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7473
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:00.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7563
p-value of test                       :  2.3e-3


-----------------------------------------------
CPU time used                    :  00:03:53.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:58.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9954


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:51.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:10.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:35.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.71
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.48
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.65
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.23
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.94
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1332.34
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7012.88
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.69
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:58.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.28
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  162.96
p-value of test                       :  4.6e-3


-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5073.93
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:12.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46503
p-value of test                       :  1.8e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870503
  j =  1                              :        399906998
  j =  2                              :            46495
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45830
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869830
  j =  1                              :        399908343
  j =  2                              :            45824
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:27.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:16.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 6.56e-3
p-value of test                       :    0.9926

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:59.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:55.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.82e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 8.93e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:35.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.06
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.07
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.91
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.40
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:50.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.48
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.51
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17329.01
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.83
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.61
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.56
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   59.41
p-value of test                       :  8.3e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.81
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.45
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.39
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.70
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.26
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.30
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.59
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.86
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.22
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.37
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.05
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  183.82
p-value of test                       :  4.0e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.67
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:46.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.58
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.75
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.11
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.64
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.43
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.26
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.19
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.10
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.92
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.62
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.90
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:14.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.68
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:12.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.58e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 7.15e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.55
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.93
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.74
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:10.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.56
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:10.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10299.75
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:42.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4707.99
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:44.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.82
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.68
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4179.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.55
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11937.00
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.45
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000032842

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.65
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000053533

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:14:10.38

 All tests were passed




Server wird beendet - Lösche Semaphor 101580800.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:42.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:34.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:52.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4432
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:53.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:01.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:01.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:52.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:57.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:11.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:35.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.28
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.39
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.40
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.54
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.87
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.03
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.87
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  372.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:46.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1441.49
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:06.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7099.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.84
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:58.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.75
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.13
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4973.07
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45735
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869735
  j =  1                              :        399908535
  j =  2                              :            45725
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45721
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869721
  j =  1                              :        399908559
  j =  2                              :            45719
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  6.4e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:27.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:18.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.80e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.68e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.67e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.37
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:36.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.32
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.47
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:50.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.30
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.99
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.07
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:30.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.71
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 2.87e-3
p-value of test                       :    0.9971

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17093.62
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.93
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.73
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.59
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.96
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.40
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.00
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.65
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.91
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.30
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.71
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:40.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.59
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.88
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.04
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.24
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.74
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:47.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.25
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.02
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.10
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.72
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:47.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.38
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.54
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.32
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.05
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.23
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.48
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.69
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.99
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.30
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.42
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.56
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:24.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.19
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :    1.76
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:15.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.90e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 9.84e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.61e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.49
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.24
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:07.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.09
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:10.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9913.99
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10083.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:42.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.18
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:44.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.23
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12003.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11759.27
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.20
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999971096

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.91
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000181978

Normal statistic for number of bits   :    1.44
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   0.081
p-value of test                       :    0.47

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:17.63

 All tests were passed




Server wird beendet - Lösche Semaphor 102957071.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:50.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997195
  j =  2                              :             1401
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:42.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7177
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:34.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4468
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:53.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4492
p-value of test                       :  9.7e-3


-----------------------------------------------
CPU time used                    :  00:01:53.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:59.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:00.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:51.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:57.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:46.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:12.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:37.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.87
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.90
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.40
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.37
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.97
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.77
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.06
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.42
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1326.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:07.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7003.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.86
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:59.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.17
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.01
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:31.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4833.41
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:06.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45911
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869911
  j =  1                              :        399908181
  j =  2                              :            45905
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46036
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870036
  j =  1                              :        399907930
  j =  2                              :            46032
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:27.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 9.22e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :  3.2e-3

Anderson-Darling statistic = A2       :    4.75
p-value of test                       :  3.8e-3


-----------------------------------------------
CPU time used                    :  00:02:19.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:01.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:38.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.24e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.47e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:40.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.38
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.68
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.20
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.52
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.11
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.86
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17603.68
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.40
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.35
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.48
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.49
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.27
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.74
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.82
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.77
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.12
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.52
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.68
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.07
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.75
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.20
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.85
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.00
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.61
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.86
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.27
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.86
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.07
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.72
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.48
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4890.72
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.80
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.31
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.56
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:25.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.20
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:16.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.54e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.14
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.81
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:08.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.13
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:09.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9855.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10276.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:45.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4762.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:45.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.13
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4292.26
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.57
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11572.94
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11619.90
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.76
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999893978

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.90
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000061561

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:26.90

 All tests were passed




Server wird beendet - Lösche Semaphor 103809039.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5392
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:46.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:38.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:38.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:05.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:04.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:59.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:01.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9955

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:12.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:42.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.65
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.89
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.33
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1565.50
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:02:21.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7197.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:51.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.27
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.15
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:10.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.35
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.40
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:38.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5126.42
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:20.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45887
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869887
  j =  1                              :        399908233
  j =  2                              :            45873
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45440
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869440
  j =  1                              :        399909124
  j =  2                              :            45432
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:30.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:19.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9925

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:48.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:03.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:58.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:37.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.041
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.67
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.90
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.57
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.32
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.74
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.40
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.61
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.65
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.35
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17527.17
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.72
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.86
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.21
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.28
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.48
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.55
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.09
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.09
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.69
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.86
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.52
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.01
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.59
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.88
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:47.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.08
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.95
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.73
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.19
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.77
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  324.87
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.17
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5085.24
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.63
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.95
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.84
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.52
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4867.15
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.11
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.16
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.09
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:24.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.28
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:25.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.94e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.14
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.27
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.25
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:07.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.93
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:10.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:04:15.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.66
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:51.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4698.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:53.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.29
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11738.73
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11801.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:32.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.34
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000009304

Normal statistic for number of bits   :   0.074
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.97
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000201652

Normal statistic for number of bits   :    1.59
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.24
p-value of test                       :    0.01

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.73

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:11.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:54.14

 All tests were passed




Server wird beendet - Lösche Semaphor 104824847.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9934


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:48.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:37.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:36.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:54.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4461
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:55.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:02.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7145
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:02.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:52.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:01.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:13.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     175
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:41.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.67
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.73
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.41
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.11
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.08
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.26
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.63
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:08.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6871.79
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.72
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   84.82
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:57.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.24
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.13
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4990.72
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:02.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45577
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869577
  j =  1                              :        399908847
  j =  2                              :            45575
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45881
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869881
  j =  1                              :        399908241
  j =  2                              :            45875
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:26.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:17.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :  9.8e-4    *****

Anderson-Darling statistic = A2       :    6.35
p-value of test                       :  7.0e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  3.5e-4    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:59.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.46e-4
p-value of test                       :    0.9994    *****

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:37.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.20e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.32e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 6.07e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:33.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.52
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.58
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.28
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.95
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.66
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.25
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17186.90
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.32
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.57
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.28
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.54
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.72
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.14
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.93
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.38
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.17
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.36
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.59
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.45
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.71
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.33
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.13
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.82
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.23
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  430.72
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.19
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.43
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.28
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.25
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.66
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.46
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  159.11
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.66
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.90
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.37
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.59
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.45
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.09
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:24.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.65
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:23.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 7.22e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.38e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.84
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.49
p-value of test                       :    0.9928

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.85
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:10.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:08.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10182.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10118.91
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:45.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4956.00
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.17
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4309.75
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.87
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.88
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11719.77
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.63
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999907439

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.01
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999864758

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.32e-3
p-value of test                       :    0.9966

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.48
p-value of test                       :  6.5e-3

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:10.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 48  MaxOft, t = 24                  3.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 106201103.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5321
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:51.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:36.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:02.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:02.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:52.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:00.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     854
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:12.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:41.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.68
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.36
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.98
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.12
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.73
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  388.11
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.39
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:08.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7071.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.22
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:03.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.62
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.18
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:32.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5027.52
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:57.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45649
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869649
  j =  1                              :        399908704
  j =  2                              :            45645
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45341
p-value of test                       :    0.9941


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869341
  j =  1                              :        399909318
  j =  2                              :            45341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:26.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:17.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:59.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:57.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:38.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.27e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:34.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.25
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   15.87
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.61
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.79
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.13
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.10
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:40.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17667.09
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.91
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    9.57
p-value of test                       :    0.9977


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.44
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.97
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.78
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.82
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.17
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.52
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.38
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.49
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.08
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.20
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.22
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.73
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.76
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.15
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  420.33
p-value of test                       :    0.9959


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.20
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.26
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.70
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.39
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.02
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.38
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  268.95
p-value of test                       :  8.2e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.24
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.08
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.01
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.97
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.81
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.30
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:24.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.75
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:23.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.63
p-value of test                       :    0.05

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.26e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.19e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 6.32e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.35
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.19
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:06.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.45
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:06.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10263.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9835.72
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:41.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5001.93
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.98
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.53
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.69
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12051.71
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11504.38
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.54
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999893222

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.43
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000091138

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.077
p-value of test                       :    0.47

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:03.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 63  WeightDistrib, r = 10           0.9991 
 78  RandomWalk1 C (L=10000, r=0)    8.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 107053071.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5514
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:53.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:03.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:03.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:54.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:59.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    3.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:12.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.52
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    2.45
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:39.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   19.49
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.36
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.10
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.16
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.80
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.68
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.59
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.23
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:12.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7322.26
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.00
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:58.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.84
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.72
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5022.36
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:15.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45599
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869599
  j =  1                              :        399908805
  j =  2                              :            45593
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45942
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869942
  j =  1                              :        399908117
  j =  2                              :            45940
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:26.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.10
p-value of test                       : 1 -  4.4e-5    *****


-----------------------------------------------
CPU time used                    :  00:02:18.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 2.13e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.05
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.96
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.58
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.15
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.34
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.19
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.65
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:39.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17376.57
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.48
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.92
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.35
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.07
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.23
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.14
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.81
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.51
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.17
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.62
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.81
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.93
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.09
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.00
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.62
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.63
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.34
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.34
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.09
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.45
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.25
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5244.18
p-value of test                       :  8.0e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.66
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.37
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.50
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.57
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.61
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.99
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.03
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.92
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:21.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.19
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -1.34
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:21.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.56e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.19
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.27
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:05.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.24
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.59
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:42.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.48
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:46.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4993.43
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.11
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.57
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11665.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11564.63
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.19
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000029440

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.32
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000110140

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.08e-4
p-value of test                       :    0.9994    *****

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.50
p-value of test                       :  6.3e-3

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:20.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 47  MaxOft AD, t = 16              1 -  4.4e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 107970575.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5479
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:55.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:05.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:55.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:59.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    2.42
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    3.01
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:45.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.28
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    3.07
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:14.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:44.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.93
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.70
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.21
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.98
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.13
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.16
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  503.71
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1508.92
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:06.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7074.51
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.76
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.01
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:59.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.74
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.87
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4938.84
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:55.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45534
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869534
  j =  1                              :        399908935
  j =  2                              :            45528
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45964
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869964
  j =  1                              :        399908078
  j =  2                              :            45952
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:26.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:17.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:00.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:58.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:35.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.78
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.71
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.14
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.65
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.63
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.34
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.66
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:51.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.40
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.88
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:40.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17429.58
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.83
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.62
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.47
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.06
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.75
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.86
p-value of test                       :    0.9951


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.75
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.48
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.04
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.04
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.13
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.51
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.40
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.84
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.91
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.01
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.62
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.50
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.87
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.64
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.62
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.37
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.05
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.05
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.12
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.93
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.16
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.33
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.96
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.49
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.18
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:22.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.91
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    3.00
p-value of test                       :  1.4e-3



-----------------------------------------------
CPU time used                    :  00:02:23.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 6.97e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.43
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.17
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.43
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:05.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10195.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:42.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5016.77
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.44
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4224.66
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.63
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11572.76
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.59
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999987923

Normal statistic for number of bits   :  -0.095
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.23
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999835046

Normal statistic for number of bits   :   -1.30
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.98
p-value of test                       :  9.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.63
p-value of test                       :  4.2e-3

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9945

Tests on the sum of all N observations
Standardized normal statistic         :  -0.013
p-value of test                       :    0.51

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:11.03

 All tests were passed




Server wird beendet - Lösche Semaphor 108986383.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:48.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:55.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4488
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:39.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:05.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:56.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:59.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.61
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.05
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    2.32
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.91
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:15.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:43.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.10
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.07
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.70
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.63
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.65
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.11
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.87
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  197.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1486.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:11.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7076.03
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.53
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.81
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:00.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.97
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.02
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:32.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4851.59
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:58.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46071
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870071
  j =  1                              :        399907863
  j =  2                              :            46061
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45419
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869419
  j =  1                              :        399909163
  j =  2                              :            45417
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:26.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:18.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.96e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.83
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.99
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.82
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.35
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.23
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:50.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.16
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.36
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.70
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17403.38
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.32
p-value of test                       :    0.9909


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.30
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.32
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.68
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.98
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.15
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.00
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.12
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.94
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.55
p-value of test                       :  6.8e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.69
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.92
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.33
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.97
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.50
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  177.08
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.88
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.68
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.38
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5111.15
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  434.31
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.88
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.66
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.22
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.49
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.92
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.41
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.47
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:24.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.64
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :  -0.095
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:22.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.40e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 9.78e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.57e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 5.45e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.00
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.49
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.76
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:03.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:05.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9971.87
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10128.54
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.079
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:43.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5048.48
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4761.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4278.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.36
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11885.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.93
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999889844

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.59
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999975917

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:09.71

 All tests were passed




Server wird beendet - Lösche Semaphor 109969423.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:47.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:55.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:58.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:06.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:06.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:56.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:59.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:46.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.95
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:15.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.86
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.05
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.19
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.66
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.83
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.93
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.51
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:45.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1381.74
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:06.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7124.42
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.19
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.33
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:24.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.15
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.02
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:33.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4974.22
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:54.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46117
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870117
  j =  1                              :        399907768
  j =  2                              :            46113
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45652
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869652
  j =  1                              :        399908701
  j =  2                              :            45642
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:26.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:18.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:01.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:38.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 5.39e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:26.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:22.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.97
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.27
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.86
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.55
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.02
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:50.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.53
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.30
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.90
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17635.71
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.03
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.18
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.86
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.12
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.85
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.28
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.42
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.99
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.49
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.94
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.15
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.67
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.85
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.09
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.91
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.07
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.47
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.91
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.11
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.74
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.09
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.02
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.79
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.96
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  447.44
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.56
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.33
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.68
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.94
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:22.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.75
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :   0.034
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:22.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.53e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.27
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.36
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.75
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.70
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:08.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.6e-3

Anderson-Darling statistic = A2       :    4.33
p-value of test                       :  6.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10367.56
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9821.23
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:40.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.36
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5000.79
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.86
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.57
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11764.42
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11863.65
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.34
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000054544

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.18
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000076159

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.84e-4
p-value of test                       :    0.9994    *****

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.32
p-value of test                       :    0.99

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:47.59

 All tests were passed




Server wird beendet - Lösche Semaphor 110919695.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:47.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5349
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:55.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4526
p-value of test                       :  2.2e-3


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7541
p-value of test                       :  4.9e-3


-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:57.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:06.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:08.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:59.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:59.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9915


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9904

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:15.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:44.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.91
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.38
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.85
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.41
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.90
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.72
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1357.78
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:11.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7035.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:00.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.28
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  158.17
p-value of test                       :  9.5e-3


-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.65
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:58.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46148
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870148
  j =  1                              :        399907710
  j =  2                              :            46136
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45933
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869933
  j =  1                              :        399908140
  j =  2                              :            45921
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:26.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:18.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:57.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:38.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.88e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:33.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.68
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.67
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.93
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.48
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.48
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.50
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.75
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17082.33
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.89
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.41
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.92
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.93
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.56
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.91
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.31
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.09
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.02
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.31
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.98
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.13
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.84
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.94
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  124.12
p-value of test                       :  2.4e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.48
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.10
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  574.00
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.00
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  110.06
p-value of test                       :  4.2e-3


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  323.35
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.86
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5111.87
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.48
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.24
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.37
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.57
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.33
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.91
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.57
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:25.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.00
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    1.46
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:21.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.70e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.68e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.72
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.84
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.83
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:05.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.36
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.09
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9909.41
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:45.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4712.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.39
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3996.96
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11987.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11999.21
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.86
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000035293

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.22
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999923759

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:52.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 C (L=1000, r=0)     2.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 111935503.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5357
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:56.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:41.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:59.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:08.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:08.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:00.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:03.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.96
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:15.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:43.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.27
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.50
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.68
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.70
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.45
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.40
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.79
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.99
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:07.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7081.75
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.59
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.31
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:47.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.10
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:39.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5142.90
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:11.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46077
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870077
  j =  1                              :        399907849
  j =  2                              :            46071
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45847
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869847
  j =  1                              :        399908310
  j =  2                              :            45839
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:28.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:19.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:04.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:57.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:01:39.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.84
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:42.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.25
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.43
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:51.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.6e-3

Kolmogorov-Smirnov- statistic = D-    : 8.87e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    4.27
p-value of test                       :  6.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   19.33
p-value of test                       :    0.9976

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.82
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.26
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17278.36
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.76
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.65
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.63
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.09
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.91
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.82
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.30
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.97
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.37
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.81
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.85
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.39
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.59
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.66
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.11
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.43
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.71
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.87
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.83
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.42
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.36
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.92
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.13
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.88
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.10
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.26
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.71
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.12
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:23.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.28
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:22.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 2.55e-3
p-value of test                       :    0.9974

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -2.14
p-value of test                       :    0.98

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    2.41
p-value of test                       :  1.0e-2

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 5.01e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.02
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.89
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:04.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.32
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:06.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.94
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.50
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:04:16.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.09
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:52.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.20
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.71
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.87
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11747.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:34.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12083.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:36.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.75
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999965717

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.01
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999972077

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:12.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:07.47

 All tests were passed




Server wird beendet - Lösche Semaphor 112918543.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:41.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:58.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:04.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:06.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:58.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7146
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:02.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.87
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     943
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    4.88
p-value of test                       :  3.3e-3

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.12
p-value of test                       :  7.8e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.64
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:13.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:43.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.49
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.16
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.28
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.98
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  370.30
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.85
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7188.43
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:00.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.70
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.61
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4933.92
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:56.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46143
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870143
  j =  1                              :        399907718
  j =  2                              :            46135
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45815
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869815
  j =  1                              :        399908373
  j =  2                              :            45809
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:25.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:16.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  9.3e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:59.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:58.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:37.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : 4.50e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.054
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:40.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.80
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.16
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.74
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.57
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.62
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.48
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.16
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17467.92
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.98
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.34
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.44
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.47
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.63
p-value of test                       :    0.9957


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.60
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.69
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.55
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.11
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.88
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.64
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.51
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.77
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.74
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.60
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.98
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.53
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.80
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.37
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.40
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5105.65
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.66
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.18
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.70
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4788.16
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  429.23
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.70
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.55
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:24.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.03
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:23.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 4.93e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.36e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.56
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.30
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:04.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.87
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:06.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10055.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.45
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:41.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.55
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:45.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.05
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.06
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.68
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.56
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11665.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.17
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999931514

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.05
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999932084

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:59.60

 All tests were passed




Server wird beendet - Lösche Semaphor 114098191.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5347
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:56.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:58.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:07.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:58.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:03.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:15.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:39.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.53
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.30
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.37
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  195.06
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.57
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.30
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7368.11
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:00.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.26
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.35
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:32.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5140.32
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:01.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45587
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869587
  j =  1                              :        399908832
  j =  2                              :            45575
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45751
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869751
  j =  1                              :        399908499
  j =  2                              :            45749
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:25.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:17.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:46.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.57e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:32.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.18
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.75
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.55
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.41
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.68
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.03
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17239.71
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.45
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.42
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.68
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.44
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.46
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.96
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.64
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.34
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.30
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.28
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.03
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.06
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.08
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.93
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.09
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.32
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.68
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.46
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.32
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.71
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.63
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.80
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.14
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.93
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.24
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.32
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.71
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.34
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.25
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:24.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.59
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:25.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 5.16e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.21e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.97
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.44
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.21
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:06.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10129.29
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10148.73
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:39.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.66
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:45.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.42
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4048.46
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4028.27
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11803.65
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12029.51
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.45
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999959954

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.99
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000035584

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.41e-3
p-value of test                       :    0.9943

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.80
p-value of test                       :    0.04

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.19
p-value of test                       :    0.01

Sample variance                       :    2.62
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:57.76

 All tests were passed




Server wird beendet - Lösche Semaphor 115113999.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:58.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7188
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:05.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:06.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:58.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:02.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    2.28
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:14.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.50
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    5.35
p-value of test                       :  2.0e-3

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:44.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.13
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.39
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.73
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.61
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.30
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.24
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.96
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.73
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.17
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.86
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:44.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:05.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6971.77
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:00.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.58
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.72
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:32.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4895.45
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:11.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:01.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45717
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869717
  j =  1                              :        399908568
  j =  2                              :            45713
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45833
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869833
  j =  1                              :        399908339
  j =  2                              :            45823
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.59e-3
p-value of test                       :    0.9915

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:26.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:17.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.77e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:27.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:41.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.12
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.74
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.04
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:39.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17378.66
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.86
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.74
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.20
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.17
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.24
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.46
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.74
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.21
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.52
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.00
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.85
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.48
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.68
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.13
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.94
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.93
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.99
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.61
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:48.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.23
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.57
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5201.97
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.79
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.87
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.30
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.20
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.11
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.21
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.88
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.62
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:25.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.10
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:24.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.71
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.06
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.43
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.85
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:05.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.08
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:43.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4769.16
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:46.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.40
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.57
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.92
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11923.81
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11917.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.59
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000005662

Normal statistic for number of bits   :   0.045
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.09
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999871994

Normal statistic for number of bits   :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.93
p-value of test                       :  9.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.24
p-value of test                       :    0.99

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:35.78

 All tests were passed




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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5488
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:57.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:43.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:59.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:59.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:07.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:08.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:01.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:06.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    5.29
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    2.07
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.15
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:13.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:41.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.72
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.57
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.67
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.33
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.25
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.05
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.23
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.06
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1490.77
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:06.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7114.46
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.50
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:13.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.46
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:47.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.87
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:38.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5033.67
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:01.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45991
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869991
  j =  1                              :        399908022
  j =  2                              :            45983
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46031
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870031
  j =  1                              :        399907942
  j =  2                              :            46023
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  6.7e-3

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:27.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:19.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.78e-3
p-value of test                       :    0.9948

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:03.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:59.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.71e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.91e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.59
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.26
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.46
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.81
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.22
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:51.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.97
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.41
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.59
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.05
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17272.39
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.49
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.55
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.96
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.41
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.57
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.39
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.20
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.42
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.29
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.36
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.55
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.53
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.71
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.53
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.70
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.97
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.70
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.70
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.43
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.05
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.73
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4900.53
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.78
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  162.04
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.33
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.03
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.64
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.96
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.28
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.42
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :   -1.27
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:21.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.10
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:22.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.36e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.38e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.77
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.12
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:04.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:06.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.88
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.92
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:04:16.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.33
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:54.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5022.28
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:56.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.79
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3988.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.51
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:33.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.40
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.77
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999985736

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.91
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000089662

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:03.34

 All tests were passed




Server wird beendet - Lösche Semaphor 117080079.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5433
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:55.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:42.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:07.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:07.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:58.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:00.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9962

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    3.22
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:45.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:13.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    2.40
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:42.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.28
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.34
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.87
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.25
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.44
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.59
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1516.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7097.25
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.86
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.82
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:02.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.98
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.94
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5059.49
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:55.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46004
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870004
  j =  1                              :        399907996
  j =  2                              :            45996
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46256
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870256
  j =  1                              :        399907490
  j =  2                              :            46252
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:26.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:17.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 2.76e-3
p-value of test                       :    0.9971

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:59.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:39.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.36e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 1.99e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:36.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.42
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.15
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.09
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.30
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.28
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.75
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.24
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.30
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   12.35
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17313.45
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.26
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.99
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.97
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.40
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.30
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.74
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.97
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.42
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.67
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.10
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.03
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.87
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.49
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.59
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.83
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.04
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.04
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.44
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.32
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.45
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.48
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.65
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.34
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.90
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.03
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.69
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.89
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.87
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.35
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.96
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:23.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.32e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 6.89e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.63e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.86
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.16
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.48
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:08.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.66
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:07.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.06
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10083.36
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:39.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4792.48
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:47.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.75
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.77
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4220.60
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11573.90
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.42
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.00
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000071356

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.59
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000038290

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.43

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:48.82

 All tests were passed




Server wird beendet - Lösche Semaphor 118161423.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:56.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:44.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4491
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:59.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:08.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:09.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:02.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:04.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.08
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9970


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    2.75
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:14.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    2.30
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:41.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.28
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.12
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.80
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.10
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.13
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.61
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  389.28
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.05
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:04.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6807.35
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:52.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.47
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:04.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:46.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.85
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:34.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5137.21
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9942


-----------------------------------------------
CPU time used                    :  00:02:57.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45760
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869760
  j =  1                              :        399908483
  j =  2                              :            45754
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45623
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869623
  j =  1                              :        399908759
  j =  2                              :            45613
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:26.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:19.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:48.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:03.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:58.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 4.86e-3
p-value of test                       :    0.9947

Anderson-Darling statistic = A2       :    3.83
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:38.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 6.87e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.99e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:40.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:39.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.09
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.60
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.63
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.04
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.42e-3
p-value of test                       :    0.9932

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  167.94
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17819.81
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.94
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.41
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.44
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.92
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.27
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.74
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.66
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.28
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.58
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.92
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.79
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.99
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.04
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.43
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.98
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.99
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.84
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.72
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.92
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.66
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.89
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4871.82
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.05
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.07
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.85
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.61
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.18
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.70
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.07
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:23.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.97
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:25.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 4.56e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.89e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.14
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.76
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.11
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:06.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9854.94
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10259.67
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:04:06.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.77
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:51.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.29
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.52
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11968.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.91
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.47
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000011167

Normal statistic for number of bits   :   0.088
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.69
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000147991

Normal statistic for number of bits   :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.014
p-value of test                       :    0.51

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:23.38

 All tests were passed




Server wird beendet - Lösche Semaphor 119177231.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:58.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:42.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4476
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:08.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:08.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:01.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:06.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     339
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:14.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:42.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.98
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.11
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.35
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.04
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.53
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.22
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1466.04
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7194.37
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.90
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:10.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.98
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.72
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5039.53
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:08.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46067
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870067
  j =  1                              :        399907869
  j =  2                              :            46061
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45797
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869797
  j =  1                              :        399908409
  j =  2                              :            45791
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:30.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:19.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:07.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.14e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.80e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.54
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.38
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.36
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.44
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.63
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9937

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17410.24
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.28
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.59
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.29
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.11
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.38
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.58
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.04
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.28
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.60
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.28
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.13
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.28
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.51
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.55
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.17
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.30
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.03
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.45
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.49
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.02
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.90
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5126.09
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.54
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.84
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.32
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.74
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.24
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.98
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.09
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.69
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:23.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.69
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -1.40
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:23.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    2.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.96e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.23e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.48
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.17
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.55
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10271.42
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10292.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:04:14.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.69
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:54.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5006.74
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:55.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.06
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11913.31
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:31.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11943.64
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:34.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.18
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999825812

Normal statistic for number of bits   :   -1.38
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.50
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999973022

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.42
p-value of test                       :    0.9922

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:45.11

 All tests were passed




Server wird beendet - Lösche Semaphor 120225807.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1470
p-value of test                       :  2.4e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334590
  j =  1                              :        599997060
  j =  2                              :             1470
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5563
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:57.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:07.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:08.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:02.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:04.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    3.11
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     825
p-value of test                       :    0.9940

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.81
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:13.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.73
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    2.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.39
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.28
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    5.70
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.22
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.55
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.13
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  384.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1375.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6971.05
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:53.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.48
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.09
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:03.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.73
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:46.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.85
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4923.25
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:59.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45984
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869984
  j =  1                              :        399908035
  j =  2                              :            45978
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869892
  j =  1                              :        399908219
  j =  2                              :            45886
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:28.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:18.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:03.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:58.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:37.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.42e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:42.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:40.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.27
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.27
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.05
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.10
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.37
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.07
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.72
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.91
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.13
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17569.35
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:52.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.63
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.89
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.09
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.54
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.24
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.98
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.79
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.57
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.85
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.48
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.86
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.34
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.53
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.19
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.28
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.78
p-value of test                       :    0.9950


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.76
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.36
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.97
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.33
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.03
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.17
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  327.73
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.17
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.88
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.12
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5100.00
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.78
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.15
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.92
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -1.72
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:20.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.56
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:20.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.12e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 8.09e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.08
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.61
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.12
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.25
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10241.28
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9814.57
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:23.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.55
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:41.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.37
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3996.84
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4028.07
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11934.23
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11948.87
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.60
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999995165

Normal statistic for number of bits   :  -0.038
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.72
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999954632

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.90
p-value of test                       :    0.97

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   0.099
p-value of test                       :    0.46

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:14.29

 All tests were passed




Server wird beendet - Lösche Semaphor 121274383.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5322
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:35.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:33.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:54.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:59.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:59.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:53.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:59.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.57
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:12.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:33.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.12
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.52
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.98
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.55
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.06
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.57
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.38
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.67
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:51.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.63
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:02.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6940.82
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:01.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.89
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.07
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:35.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4917.16
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:12.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45780
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869780
  j =  1                              :        399908442
  j =  2                              :            45776
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46216
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870216
  j =  1                              :        399907570
  j =  2                              :            46212
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:27.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:17.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:51.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:34.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 4.20e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:34.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.055
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.64
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.94
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.38
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.69
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.45
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.16
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.95
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:43.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.95
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:32.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.23
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.83
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17447.90
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.45
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.23
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.39
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.72
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.67
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:40.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.09
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.60
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.84
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.86
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.03
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:40.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.06
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.24
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.26
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.47
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.22
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.62
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.19
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.69
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.19
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.31
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.29
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.56
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.07
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.66
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.01
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  319.22
p-value of test                       :    0.9930


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.26
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.57
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.00
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.59
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.47
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:14.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.00
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:12.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 3.57e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.79e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 3.53e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.90
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.49
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.64
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:09.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.44
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:10.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.92
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9820.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.49
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:44.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.58
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.31
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.73
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.26
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.74
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.71
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.30
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000050485

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.83
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999975686

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:14:18.88

 All tests were passed




Server wird beendet - Lösche Semaphor 101613569.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5338
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:42.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:34.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:53.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:53.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:00.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:00.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:52.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:58.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    2.90
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     554
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    4.76
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    2.12
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:10.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:35.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.26
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.73
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.09
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.83
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.05
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.21
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.10
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.27
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.12
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7142.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.26
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:01.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.11
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:35.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4978.76
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:18.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45726
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869726
  j =  1                              :        399908550
  j =  2                              :            45722
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46103
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870103
  j =  1                              :        399907800
  j =  2                              :            46091
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:28.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:18.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 4.03e-3
p-value of test                       :    0.9956

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:44.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:53.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.39e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.095
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.032
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:34.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.16
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.12
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.03
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.09
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.28
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:41.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 3.54e-3
p-value of test                       :    0.9963

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.27
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:29.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.11
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17764.65
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.38
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.68
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.90
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.10
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:40.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.83
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.09
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.84
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.58
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.90
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.15
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.36
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.08
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.36
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:47.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.88
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.01
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.87
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.86
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.25
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.76
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.04
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.79
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.40
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.46
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.96
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.31
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5153.86
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.32
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.79
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :   -1.96
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:16.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.08
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -1.40
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:15.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.31e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.10e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.62
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.91
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.41
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:06.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:09.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10173.04
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.28
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:45.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4786.46
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:49.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.84
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11720.82
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11969.93
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.04
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999905552

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.51
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999802337

Normal statistic for number of bits   :   -1.56
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:39.13

 All tests were passed




Server wird beendet - Lösche Semaphor 103022593.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5479
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:43.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7524
p-value of test                       :  8.5e-3


-----------------------------------------------
CPU time used                    :  00:02:35.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:54.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:00.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:00.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:51.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:57.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:10.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.33
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    2.01
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:38.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.78
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.65
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.17
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.03
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.57
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.43
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.90
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.03
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.64
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.83
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7194.19
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.76
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:01.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.37
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:46.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.67
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:34.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5071.26
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:18.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46009
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870009
  j =  1                              :        399907983
  j =  2                              :            46007
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45537
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869537
  j =  1                              :        399908928
  j =  2                              :            45533
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:28.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :  1.4e-3

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:19.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:45.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:53.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:32.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 8.26e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:38.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:34.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.46
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.03
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.90
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.89
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.30
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.82
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:43.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.97
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.1e-3

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.99
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :  1.3e-3

Anderson-Darling statistic = A2       :    5.59
p-value of test                       :  1.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17988.01
p-value of test                       :  1.5e-3



-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.06
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.83
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.53
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.79
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.29
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.01
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.41
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    6.46
p-value of test                       :    0.9999    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.36
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.33
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.32
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.94
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.42
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.15
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.15
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.26
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.03
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.14
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.91
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.81
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.77
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5112.83
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.90
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.47
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.21
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.71
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4707.88
p-value of test                       :    0.9985


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.81
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.36
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.52
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :  -0.051
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:16.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.63
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:18.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.12
p-value of test                       :    0.98

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.46e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.53e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.82
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.15
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.65
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:09.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.59
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:08.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10055.47
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10214.72
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:57.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.70
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.60
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.54
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.28
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11817.68
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.72
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999979370

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.91
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999999536

Normal statistic for number of bits   : -3.67e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:27.44
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 R (L=50, r=25)      0.9999 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 104005633.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1504
p-value of test                       :  1.0e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334624
  j =  1                              :        599996992
  j =  2                              :             1504
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5386
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:46.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4533
p-value of test                       :  1.6e-3


-----------------------------------------------
CPU time used                    :  00:01:38.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:37.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:55.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:00.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:01.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:51.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:57.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    2.29
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:46.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     272
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:05.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    2.02
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:34.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.03
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.58
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.54
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.45
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.85
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   85.49
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.51
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.24
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:02.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7164.70
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:45.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.51
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.44
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:04.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.48
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.56
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:32.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4861.92
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:58.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46228
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870228
  j =  1                              :        399907546
  j =  2                              :            46224
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46267
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870267
  j =  1                              :        399907471
  j =  2                              :            46257
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:26.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:18.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:46.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:54.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:33.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.84e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 8.36e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:34.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.13
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.04
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.41
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17673.50
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.21
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.37
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.66
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.44
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.68
p-value of test                       :    0.9951


-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.29
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.58
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.92
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.69
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.06
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.99
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.51
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.56
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.23
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.59
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.44
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.31
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.18
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.98
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.05
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.30
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.11
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.23
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.98
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.54
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.49
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.78
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.09
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.37
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.75
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:18.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.60
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:20.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 3.95e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.91
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:30.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.49
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.57
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:05.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.28
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:08.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10075.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9934.63
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:46.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.01
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.82
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.12
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11942.04
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11444.07
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:01:29.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.69
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000002725

Normal statistic for number of bits   :   0.022
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.85
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000119956

Normal statistic for number of bits   :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:38.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           1.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 105021441.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:40.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1256
p-value of test                       :    0.9984

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334376
  j =  1                              :        599997488
  j =  2                              :             1256
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1242
p-value of test                       :    0.9996    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334362
  j =  1                              :        599997516
  j =  2                              :             1242
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:51.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:59.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:00.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:51.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:57.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.30
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     550
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:11.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    3.10
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     124
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:40.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.57
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.02
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.31
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.01
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.82
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.52
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  388.27
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:46.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.80
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:02.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6929.61
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:02.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.38
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:47.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  165.37
p-value of test                       :  3.2e-3


-----------------------------------------------
CPU time used                    :  00:01:34.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5035.07
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:57.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45786
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869786
  j =  1                              :        399908433
  j =  2                              :            45776
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45862
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869862
  j =  1                              :        399908278
  j =  2                              :            45858
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:27.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:18.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:48.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:03.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  6.6e-3

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:33.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-5
p-value of test                       :    0.9918

Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:31.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:33.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.14
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.37
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.68
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.83
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.51
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:39.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.71
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.67
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.33
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.62
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.64
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17493.60
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.16
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.05
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.51
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.38
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.28
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.24
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.36
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.47
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.76
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  195.54
p-value of test                       :  3.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.42
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.40
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.43
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.28
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.46
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.96
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.38
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.29
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.69
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5112.94
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.67
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.62
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.94
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4799.93
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.01
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.21
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.74
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -1.38
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:18.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.35
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    1.97
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:20.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.91e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.49
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.90
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.80
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9812.94
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9875.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:45.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  2.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    5.23
p-value of test                       :  2.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4593.66
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4749.84
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:50.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4266.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.76
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11994.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.23
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.49
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000044440

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.16
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999960518

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:34.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 105906177.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5567
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:53.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:03.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:01.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:53.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:57.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    2.80
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:10.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.70
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.39
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.35
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.59
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.44
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.92
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.26
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  391.72
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1345.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6975.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:43.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.06
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.11
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:06.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.66
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.83
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5036.80
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:55.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46029
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870029
  j =  1                              :        399907946
  j =  2                              :            46021
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45798
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869798
  j =  1                              :        399908408
  j =  2                              :            45790
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:26.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:18.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:55.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 2.81e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:33.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:34.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.61
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.87
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.42
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.79
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.49
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.06
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.24
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9919

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17483.52
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:52.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.65
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.79
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.32
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.29
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.51
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.09
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.21
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.15
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.24
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.37
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.13
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.48
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.59
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.79
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.46
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.82
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.87
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   44.71
p-value of test                       :    0.9972


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.13
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.11
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4931.82
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.18
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.68
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.33
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.01
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.45
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.89
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.13
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.39
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:18.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.24
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :  -0.073
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:19.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    2.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 5.18e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.47e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.21
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.47
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.39e-3
p-value of test                       :    0.9932

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:05.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10133.73
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10188.56
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:42.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.40
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.78
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.39
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.24
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.07
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.05
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.91
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000056341

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.85
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000121732

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.93

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   0.051
p-value of test                       :    0.48

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:01.54

 All tests were passed




Server wird beendet - Lösche Semaphor 106889217.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1270
p-value of test                       :    0.9948

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334390
  j =  1                              :        599997460
  j =  2                              :             1270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:58.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7530
p-value of test                       :  7.0e-3


-----------------------------------------------
CPU time used                    :  00:02:44.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:09.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:09.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:02.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:02.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    4.41
p-value of test                       :  5.5e-3

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:12.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.08
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:38.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.62
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.67
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.62
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.59
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.42
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.91
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.33
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.74
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:06.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7008.42
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:57.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.63
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.12
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.47
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4816.71
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:01.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46159
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870159
  j =  1                              :        399907687
  j =  2                              :            46149
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46347
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870347
  j =  1                              :        399907313
  j =  2                              :            46333
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:31.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:21.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.5e-3

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:06.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:56.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.93e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : -6.64e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:43.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.20
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.58
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.56
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.82
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.66
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.17
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:52.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.93
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.92
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17358.32
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.58
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.92
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.11
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.23
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.94
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.02
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.26
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.89
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.93
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.75
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.24
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.47
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.67
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.79
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.52
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.09
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.37
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.35
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.65
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.09
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.85
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.36
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.04
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.51
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.29
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.66
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.73
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4904.68
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.19
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.07
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.22
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :  -0.091
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:23.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.67
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -1.84
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:21.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.9999    *****

Anderson-Darling statistic = A2       :    3.95
p-value of test                       :  9.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -3.02
p-value of test                       :    0.9987

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.71e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 8.91e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 8.03e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.14
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.89
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.66
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:07.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.73
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9869.66
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9805.30
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:04:25.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:54.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.89
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.29
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.48
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11997.80
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:34.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11967.09
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:34.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.42
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999980867

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.02
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999951134

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.12

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:40.57

 All tests were passed




Server wird beendet - Lösche Semaphor 107839489.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:50.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:53.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:04.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:54.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:00.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:13.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:38.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.52
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.88
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.64
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.01
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.13
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.64
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.31
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.76
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7022.51
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.23
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.64
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:01.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.11
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.64
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:33.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5102.75
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:17.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45487
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869487
  j =  1                              :        399909029
  j =  2                              :            45481
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45812
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869812
  j =  1                              :        399908379
  j =  2                              :            45806
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:26.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:18.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:01.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:54.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:32.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 3.53e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 8.70e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:35.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.59
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.08
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.64
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.39
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.44
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.78
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.58
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.26
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.05
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17183.94
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.49
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.75
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.90
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.76
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.10
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.72
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.90
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.86
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.96
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.38
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.43
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.06
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.88
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.83
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.34
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.27
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.56
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.41
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.96
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.60
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.75
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.01
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.64
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.96
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.25
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.41
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.43
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.27
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  252.34
p-value of test                       :  7.1e-3


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.77
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :   0.092
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:21.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.16
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:21.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 3.48e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.32
p-value of test                       :    0.9953

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.02
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.70
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:07.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:07.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.27
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9839.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.038
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:40.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4779.30
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.05
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.44
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.06
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11937.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11700.65
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.79
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999927149

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.33
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999898187

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:56.63

 All tests were passed




Server wird beendet - Lösche Semaphor 109051905.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5376
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:52.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4439
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:04.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:03.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:55.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:00.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:13.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:40.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.53
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.88
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.14
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.95
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.94
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  194.53
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.98
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1356.09
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6971.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.44
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.80
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:00.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.12
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.00
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:34.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5060.59
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:14.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46149
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870149
  j =  1                              :        399907711
  j =  2                              :            46131
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46330
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870330
  j =  1                              :        399907350
  j =  2                              :            46310
  j =  3                              :               10
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:27.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:27.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:01.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:54.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:33.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 8.00e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.79e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:33.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.16
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.15
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:48.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.44
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.39
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.06
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.21
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17271.54
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.88
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.83
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.17
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.55
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.56
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.18
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.43
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.03
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.62
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.75
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.20
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.60
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.39
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.99
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.85
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.80
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.99
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.21
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.91
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.11
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.89
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.73
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.05
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.95
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5132.46
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.59
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.49
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:34.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.23
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.47
p-value of test                       :    0.9912


-----------------------------------------------
Normal statistic for number of jumps  :   0.061
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:22.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.82
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.14
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.10
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:05.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  250.43
p-value of test                       :  8.9e-3

-----------------------------------------------
CPU time used                    :  00:02:07.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9778.34
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9918.01
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.048
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:38.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:46.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.95
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3937.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3844.42
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11956.49
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11747.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.99
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999995237

Normal statistic for number of bits   :  -0.038
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.82
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000109021

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         : -1.70e-3
p-value of test                       :    0.50

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.017
p-value of test                       :    0.51

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:10.98

 All tests were passed




Server wird beendet - Lösche Semaphor 110034945.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5437
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:53.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4452
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:05.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:05.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:55.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:00.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    3.76
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     970
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:48.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.81
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    2.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.85
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     335
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:12.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.34
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.58
p-value of test                       :  1.7e-3

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.11
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.29
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.93
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.66
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.48
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.76
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.15
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  486.08
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7118.31
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.51
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.75
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:00.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.40
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.19
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:34.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5129.29
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46037
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870037
  j =  1                              :        399907928
  j =  2                              :            46033
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45704
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869704
  j =  1                              :        399908593
  j =  2                              :            45702
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:28.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:18.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:45.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.0e-3

Kolmogorov-Smirnov- statistic = D-    : 3.52e-3
p-value of test                       :    0.9962

Anderson-Darling statistic = A2       :    4.63
p-value of test                       :  4.4e-3


-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:33.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.86e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.00e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.98e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:33.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.61
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:48.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.09
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.32
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:48.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.00
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.84
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.94
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.11
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.90
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.80
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17488.18
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.22
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.89
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.63
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.64
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.15
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.40
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.49
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.81
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.57
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.23
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.22
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.46
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.54
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.42
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.74
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.08
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.04
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.23
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.01
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.54
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.72
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.14
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4887.54
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  320.47
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.15
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.83
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.04
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.47
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.90
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  256.25
p-value of test                       :  4.4e-3


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.92
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:21.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.01
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -0.98
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:21.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 7.48e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 6.26e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.74
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.88
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.39
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:07.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:07.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9834.95
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9737.66
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:38.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.38
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4205.24
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.52
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.34
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11586.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.80
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999953354

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.14
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999915029

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   0.058
p-value of test                       :    0.48

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:00.04

 All tests were passed




Server wird beendet - Lösche Semaphor 111017985.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5493
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:53.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:57.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7115
p-value of test                       :    0.9914


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:55.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:00.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    3.42
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     826
p-value of test                       :    0.9934

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:14.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:44.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.80
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.14
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.63
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.80
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  373.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1351.05
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7023.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.91
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.14
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:02.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.55
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.12
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:31.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5113.96
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45824
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869824
  j =  1                              :        399908361
  j =  2                              :            45806
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45938
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869938
  j =  1                              :        399908128
  j =  2                              :            45930
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:27.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:18.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.76
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:01.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:01:54.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:32.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-5
p-value of test                       :    0.9921

Kolmogorov-Smirnov- statistic = D-    : 2.69e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:34.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:34.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.43
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.14
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.75
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:47.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.94
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.61
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.82
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17667.77
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.65
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.01
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.38
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.57
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.62
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.28
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.10
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.30
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.20
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.86
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.04
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.74
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.60
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.60
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.04
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.70
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.20
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.53
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.82
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.15
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.81
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.50
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.73
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.61
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.16
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.95
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.66
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.84
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.40
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:34.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.57
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:19.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.95
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:20.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         : -5.43e-3
p-value of test                       :    0.50

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.20e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 6.66e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.10e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.97
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.83
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.09
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:04.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.00
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:06.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10098.40
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10023.40
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:42.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4933.58
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.66
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:49.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.92
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.79
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12002.32
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.16
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000056707

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.41
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000051406

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.21
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.074
p-value of test                       :    0.53

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:45.96

 All tests were passed




Server wird beendet - Lösche Semaphor 111968257.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5512
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:53.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:06.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:06.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:55.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:59.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.44
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    3.26
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.93
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:15.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:41.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.86
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.97
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.44
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.54
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  179.89
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.82
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1495.05
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7052.85
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:42.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.62
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.86
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.49
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5066.78
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:54.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45616
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869616
  j =  1                              :        399908773
  j =  2                              :            45606
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46161
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870161
  j =  1                              :        399907680
  j =  2                              :            46157
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:26.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:17.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:54.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:34.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 3.84e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.66e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.053
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:33.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:35.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  100.01
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.59
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.62
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.54
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:37.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.45
p-value of test                       :  6.0e-3

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.76
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17185.92
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.12
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.47
p-value of test                       :    0.9904


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.28
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.09
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.21
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.48
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.72
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.40
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.23
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.96
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.05
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.11
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.91
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.00
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.08
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.31
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.03
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.87
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.64
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.91
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.67
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.12
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.19
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.25
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  458.33
p-value of test                       :  5.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4898.43
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.03
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.14
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.52
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    1.23
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:21.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.25
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:21.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    1.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 7.87e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.78
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.00
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.48
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:04.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.27
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:04.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10196.32
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 2.19e-3
p-value of test                       :    0.9978

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9726.35
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.079
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:39.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4761.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:47.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5048.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.82
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3944.68
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11780.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11942.27
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.08
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000155869

Normal statistic for number of bits   :    1.23
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.56
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000065293

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.15

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.6e-3

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.69
p-value of test                       :    0.95

Sample variance                       :    0.19
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:11.51

 All tests were passed




Server wird beendet - Lösche Semaphor 112984065.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:27.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:55.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:06.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:05.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:55.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:00.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    2.13
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:14.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:41.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.41
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.67
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.51
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.33
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.76
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.79
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1467.01
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7085.02
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.29
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:08.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.24
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.02
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4910.13
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:11.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:53.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45647
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869647
  j =  1                              :        399908710
  j =  2                              :            45639
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45899
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869899
  j =  1                              :        399908206
  j =  2                              :            45891
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:25.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:17.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:02.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:54.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.98e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.71
p-value of test                       :  3.3e-3

-----------------------------------------------
CPU time used                    :  00:00:22.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.63
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:48.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.23
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.55
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.58
p-value of test                       :    0.9917

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.72
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.48
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.95
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17398.30
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.73
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.45
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.82
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.24
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.41
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.92
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.69
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.10
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.63
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.52
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.75
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.04
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.34
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.44
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.57
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.47
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.84
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.95
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.03
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.47
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.69
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.45
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.26
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.08
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.87
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.93
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.41
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.49
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:22.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.63
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:22.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.75e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.79e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 5.91e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.05
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.49
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.68
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:04.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.81
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:05.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.12
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.40
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:41.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.52
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4239.51
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11984.41
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11644.40
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.00
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999942428

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.35
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000022237

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.57

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:42.35

 All tests were passed




Server wird beendet - Lösche Semaphor 113967105.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:48.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5386
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:53.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4444
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:06.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:05.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7529
p-value of test                       :  7.2e-3


-----------------------------------------------
CPU time used                    :  00:03:55.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:00.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.55
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:13.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.20
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:45.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.59
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.62
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.80
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.03
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.46
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  477.05
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.60
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:02.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7025.15
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.01
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:06.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.76
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.33
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:33.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4964.29
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:54.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46106
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870106
  j =  1                              :        399907791
  j =  2                              :            46100
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46429
p-value of test                       :  5.3e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870429
  j =  1                              :        399907146
  j =  2                              :            46421
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:27.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:19.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:03.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:55.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:32.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.01e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.96e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.65e-4
p-value of test                       :  4.9e-3

Kolmogorov-Smirnov- statistic = D-    : 4.85e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:33.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.41
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.92
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.10
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.85
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.59
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.79
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.61
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.43
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17680.57
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.86
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.57
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.59
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.74
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.57
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.44
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.80
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.05
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.30
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.70
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.49
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.92
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.37
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.12
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.21
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.01
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.97
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.52
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.28
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.59
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.33
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.76
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.22
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.50
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.05
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.90
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.35
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.58
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.82
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:23.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.74
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:23.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.98e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 9.15e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 9.64e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.25
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.52
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.31
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.03
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.8e-3

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10252.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.66
p-value of test                       :  4.7e-5    *****

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    5.16
p-value of test                       :  2.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9635.49
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:38.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4735.13
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.03
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11948.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:29.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.67
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000003007

Normal statistic for number of bits   :   0.024
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.57
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000012448

Normal statistic for number of bits   :   0.098
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:51.70

 All tests were passed




Server wird beendet - Lösche Semaphor 114950145.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5490
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:55.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:59.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:06.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:05.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7053
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:03:56.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:01.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    2.49
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:14.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.52
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:45.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.08
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.30
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.55
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.36
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.01
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:45.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7071.33
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.26
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.40
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:01.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.22
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.93
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:29.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5299.72
p-value of test                       :  5.2e-3


-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:57.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45593
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869593
  j =  1                              :        399908816
  j =  2                              :            45589
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46025
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870025
  j =  1                              :        399907954
  j =  2                              :            46017
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:26.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:18.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:03.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:01:54.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.68e-3
p-value of test                       :    0.9972

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:33.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 8.45e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 9.37e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:32.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:31.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.39
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.47
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.35
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:37.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.21
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.87
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.37
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17308.72
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.12
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.99
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.95
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.80
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.13
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.84
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.59
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.71
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.10
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.13
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.91
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.00
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.70
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.30
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.65
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.76
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.93
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.74
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  191.00
p-value of test                       :  1.3e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.11
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.14
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.99
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.72
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.48
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.03
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.30
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.09
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5131.61
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.94
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.30
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:23.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.08
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :    1.22
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:23.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 4.04e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.32
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.12
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.13
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:06.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.91
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:07.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.74
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10168.23
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:39.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.69
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.25
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.68
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.82
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11455.83
p-value of test                       :    0.9923

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11625.18
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.63
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000083869

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.26
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999917060

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.042
p-value of test                       :    0.48

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   0.064
p-value of test                       :    0.47

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:55.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 20  BirthdaySpacings, t = 16        0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 115933185.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5506
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:55.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:42.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:06.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:06.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:56.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:00.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.38
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9909


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    2.12
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.32
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:13.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.56
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.75
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.07
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.33
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.74
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.80
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.21
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:45.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.24
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:02.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7037.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.14
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:04.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.09
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.36
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4956.30
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:53.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46010
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870010
  j =  1                              :        399907985
  j =  2                              :            46000
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45850
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869850
  j =  1                              :        399908306
  j =  2                              :            45838
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:27.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:18.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  4.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:57.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:37.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 2.83e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:32.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:31.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.32
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:48.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.62
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.98
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.13
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.35
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.65
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.60
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17494.46
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:52.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.42
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.17
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.13
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.04
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.90
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.39
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.10
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.43
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.15
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.70
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.53
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.81
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.88
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.88
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.83
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.57
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.91
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.20
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.81
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.96
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.10
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4823.99
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.52
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.70
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.74
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.06
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.49
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.78
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.73
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:23.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.73
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:23.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.79e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.11
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.12
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:04.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  160.69
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:07.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9775.81
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9820.20
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:38.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.77
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.10
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.53
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12196.41
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11526.97
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.09
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000048913

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.98
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999981008

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         : 5.04e-3
p-value of test                       :    0.50

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:28.52

 All tests were passed




Server wird beendet - Lösche Semaphor 116916225.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1495
p-value of test                       :  2.5e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334615
  j =  1                              :        599997010
  j =  2                              :             1495
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1490
p-value of test                       :  4.1e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334610
  j =  1                              :        599997020
  j =  2                              :             1490
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:58.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7158
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4484
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:09.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:09.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:01.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:01.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.02
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:14.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    3.38
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:43.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.57
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.06
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.90
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.69
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.88
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:03.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7059.93
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:44.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.80
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.44
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:03.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.27
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  155.62
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4933.00
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:57.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45911
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869911
  j =  1                              :        399908180
  j =  2                              :            45907
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45862
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869862
  j =  1                              :        399908277
  j =  2                              :            45860
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:27.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:17.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:36.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.059
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:31.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:31.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.14
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.43
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.66
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:48.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.26
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.90
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.37
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.21
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17250.44
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.82
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.83
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.20
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.59
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.44
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.68
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.92
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.12
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.03
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.70
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.54
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.84
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.10
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.75
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.54
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.38
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.78
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.79
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.37
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.51
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.50
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.86
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.61
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.62
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.18
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.76
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.96
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5164.12
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.73
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.51
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.92
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:21.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.80
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:22.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.29e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 5.41e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.14
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.53
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.09
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:06.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.73
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:06.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9818.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10044.93
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:46.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4789.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3943.53
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.58
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11677.24
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11694.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:30.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.95
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999896243

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.71
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999964424

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   0.021
p-value of test                       :    0.49

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.021
p-value of test                       :    0.49

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:18.26
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           2.5e-4
 11  CollisionOver, t = 21           4.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 117932033.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:43.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4486
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:10.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:08.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:57.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:01.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    2.12
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:49.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:13.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9913


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:42.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   19.38
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.84
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.90
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.64
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.86
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:44.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.88
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7158.29
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:45.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   86.80
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:57.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.25
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.35
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5146.39
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:11.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:56.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46574
p-value of test                       :  6.1e-4    *****


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870574
  j =  1                              :        399906852
  j =  2                              :            46574
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908180
  j =  2                              :            45910
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:27.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:17.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.89
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  9.5e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:01.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.00e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.076
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:31.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.35
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.86
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.27
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.38
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.96
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:39.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.43
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.59
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.40
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17642.29
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   70.33
p-value of test                       :  3.7e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.24
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.73
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.54
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.43
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.33
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.95
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.18
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.52
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.11
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.11
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.80
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.02
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.95
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.82
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.58
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.46
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.76
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.20
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.78
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.38
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.45
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.17
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.54
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.32
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.53
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.74
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.18
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:20.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.55
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :  -0.078
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:21.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.85
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.58
p-value of test                       :    0.9951

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.60e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 8.39e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.57
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.62
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.50
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  253.76
p-value of test                       :  6.0e-3

-----------------------------------------------
CPU time used                    :  00:02:03.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:06.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10174.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10074.26
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:42.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.47
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4720.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.78
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.89
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.01
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11946.17
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.30
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000001894

Normal statistic for number of bits   :   0.015
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.10
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999879206

Normal statistic for number of bits   :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:07.44
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 44  CollisionPermut, r = 0          6.1e-4
 74  RandomWalk1 M (L=50, r=0)       3.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 118947841.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:49.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5434
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:57.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:43.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:59.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:59.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:11.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7155
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:04.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:07.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:51.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    2.94
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     556
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:17.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:43.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.79
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.39
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.23
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.83
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.63
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.90
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  269.37
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.96
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.99
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:05.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7118.72
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.00
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:08.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.85
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.62
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:36.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5150.61
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:58.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45694
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869694
  j =  1                              :        399908616
  j =  2                              :            45686
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46184
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870184
  j =  1                              :        399907637
  j =  2                              :            46174
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  7.7e-3

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:27.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:16.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:01.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.00e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.59e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.78e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.60
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:01:46.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.66
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.61
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.50
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.21
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.71
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.03
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.69
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17206.92
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.45
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.16
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.84
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.87
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.77
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.17
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.25
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.25
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.38
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.78
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.75
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.73
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.08
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.74
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.97
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.93
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.01
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.32
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.01
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.17
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.79
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.17
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.48
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.38
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.20
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.09
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.12
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.92
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :    1.55
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:20.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.76
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:21.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.33e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 6.91e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.77e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.13
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.14
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:04.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.02
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10116.94
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.055
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:20.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4749.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:53.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4956.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.21
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12111.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.83
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:33.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.47
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000046012

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.08
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999865850

Normal statistic for number of bits   :   -1.06
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.088
p-value of test                       :    0.47

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:36.34

 All tests were passed




Server wird beendet - Lösche Semaphor 119996438.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5473
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:53.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:42.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:58.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:59.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:07.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:58.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:02.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9918


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:51.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.62
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    2.84
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     552
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    3.03
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    3.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     272
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:21.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:49.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.44
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.73
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.11
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.57
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.88
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.84
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.31
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.34
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.68
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.76
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7018.36
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:44.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:02.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.15
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.27
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5176.60
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:56.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45835
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869835
  j =  1                              :        399908331
  j =  2                              :            45833
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45453
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869453
  j =  1                              :        399909095
  j =  2                              :            45451
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.35
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:27.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.4e-3

Kolmogorov-Smirnov- statistic = D-    : 7.36e-3
p-value of test                       :    0.9915

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9908


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 6.13e-3
p-value of test                       :    0.9931

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:59.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:53.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 7.73e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 3.68e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.027
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:32.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.15
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.76
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.57
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.57
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.59
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.27
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:40.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.79
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.93
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17515.13
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.61
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.16
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.48
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.51
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.93
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.41
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.05
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.15
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.87
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.59
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.77
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.54
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.18
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.33
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.17
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.41
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.07
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.30
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.48
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.89
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.97
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5183.95
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.08
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.97
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.26
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.88
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.76
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.03
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.99
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:19.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.43
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:20.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.70e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.80
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.82
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:05.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:05.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10238.94
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9931.23
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.081
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:38.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4997.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.80
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4282.18
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.56
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11850.67
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.36
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999870929

Normal statistic for number of bits   :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.21
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999915137

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   0.084
p-value of test                       :    0.47

Sample variance                       :    2.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9945

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:20.97

 All tests were passed




Server wird beendet - Lösche Semaphor 121045014.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:40.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:35.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:34.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4461
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:54.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:59.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:59.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:52.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:58.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.66
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:10.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    3.61
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     121
p-value of test                       :    0.9916

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:35.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.72
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.81
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.84
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.55
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.17
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.73
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.96
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7045.51
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:51.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.10
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.14
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:01.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.99
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.03
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5060.49
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46182
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870182
  j =  1                              :        399907638
  j =  2                              :            46178
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46322
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870322
  j =  1                              :        399907360
  j =  2                              :            46314
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:27.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:15.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:59.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:52.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:33.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.68e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.026
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.97
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.28
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.45
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.67
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.01
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.67
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:42.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.86
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.9e-3

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    4.32
p-value of test                       :  6.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   19.89
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.72
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:30.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   97.19
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17343.82
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:55.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.27
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.98
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.77
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.94
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.74
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.37
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.40
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.42
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.95
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.80
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.72
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.27
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.02
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.80
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.26
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.29
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.73
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.17
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.76
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.86
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:47.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.11
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.59
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.60
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  436.81
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.12
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.01
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.66
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.28
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.42
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.23
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    1.43
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:13.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.69
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:11.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.20e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 8.11e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 3.86e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.26
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.24
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.25
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:11.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:11.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.69
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:43.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.81
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:48.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.53
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4235.17
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3971.26
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12016.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11977.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.83
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999932381

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.64
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000055408

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.16
p-value of test                       :    0.98

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:14:09.90

 All tests were passed




Server wird beendet - Lösche Semaphor 101646338.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:42.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:36.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:34.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:53.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4227
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:00.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:00.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:52.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:57.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.00
p-value of test                       :  3.1e-3

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:10.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:38.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.75
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.44
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.15
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.48
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.32
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  283.20
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:45.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.88
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7045.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.84
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:03.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.73
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.11
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:35.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4987.24
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:59.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45557
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869557
  j =  1                              :        399908886
  j =  2                              :            45557
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46184
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870184
  j =  1                              :        399907638
  j =  2                              :            46172
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:28.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 4.83e-3
p-value of test                       :    0.9944

Anderson-Darling statistic = A2       :    4.14
p-value of test                       :  7.5e-3


-----------------------------------------------
CPU time used                    :  00:02:19.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:00.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.09e-3
p-value of test                       :    0.9907

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:52.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:33.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.01e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:34.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.22
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.78
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.91
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.03
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.89
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:40.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.61
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.72
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17675.94
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.85
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.26
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.69
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.23
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.81
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:40.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.74
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.96
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.25
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.26
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.60
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.48
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.41
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.62
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.86
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.15
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:47.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.17
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.49
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.32
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.09
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.53
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.82
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.50
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.30
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.65
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.49
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.70
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.81
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5086.92
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.50
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.45
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.89
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -2.21
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:14.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.93
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -0.98
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:15.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.55e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 5.66e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:47.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.69
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.68
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.48
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:08.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.07
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:09.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9953.14
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.16
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:04:09.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.39
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:48.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.74
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.49
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4243.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11703.39
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11639.01
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.31
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999949424

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.63
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  8000010372

Normal statistic for number of bits   :   0.082
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :  6.3e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.9998    *****

Anderson-Darling statistic = A2       :    7.84
p-value of test                       :  1.5e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -3.92
p-value of test                       : 1 -  4.4e-5    *****

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   0.039
p-value of test                       :    0.48

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :  -0.029
p-value of test                       :    0.51

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:00.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 104  AutoCor, d=3, r=0              1 -  4.4e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 103251970.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5487
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:43.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:36.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:35.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:54.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:59.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:01.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:52.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:58.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9935

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9939


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:01.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.96
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:32.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.06
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.60
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.88
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.25
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.37
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.14
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.98
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.19
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.22
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.58
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:59.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7266.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.47
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:03.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.25
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:47.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.39
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5079.55
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:58.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46547
p-value of test                       :  9.4e-4    *****


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870547
  j =  1                              :        399906908
  j =  2                              :            46543
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45695
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869695
  j =  1                              :        399908612
  j =  2                              :            45691
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:27.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:19.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:32.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.80e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 3.01e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.017
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:34.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.58
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.75
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.22
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.01
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.94
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   48.83
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:40.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.18
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.4e-3

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.58
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17263.92
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.36
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.16
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.97
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.07
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.11
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.27
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.76
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.37
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.08
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.81
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.74
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.00
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.39
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.92
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.42
p-value of test                       :  9.0e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.42
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.99
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.20
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.61
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.07
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.37
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.00
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.09
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.28
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.11
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.79
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.99
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.66
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.00
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.28
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :   -1.62
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:16.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.71
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :   0.043
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:16.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.23
p-value of test                       :    0.01

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 6.37e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :  6.4e-3

Kolmogorov-Smirnov- statistic = D-    : 1.82e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.88
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.15
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.21
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:08.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.88
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9933.81
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:54.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.80
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.73
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11824.61
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.13
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000141304

Normal statistic for number of bits   :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.89
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999845825

Normal statistic for number of bits   :   -1.22
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:45.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 44  CollisionPermut, r = 0          9.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 104136706.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:46.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:37.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:01.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7498
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:02.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:53.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:57.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    3.12
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:45.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9914

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9949

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:11.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:38.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.64
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.23
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.61
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.05
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.01
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.15
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.55
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7029.30
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.18
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:09.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.76
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  165.54
p-value of test                       :  3.1e-3


-----------------------------------------------
CPU time used                    :  00:01:37.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5318.40
p-value of test                       :  3.1e-3


-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:03.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46109
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870109
  j =  1                              :        399907787
  j =  2                              :            46099
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45702
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869702
  j =  1                              :        399908598
  j =  2                              :            45698
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:30.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:18.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:59.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:55.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:36.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.41
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:01:43.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.48
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.21
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.67
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.65
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17564.61
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.10
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.61
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.45
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.81
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.24
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.19
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.45
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.65
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.81
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.50
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.07
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.82
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.06
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.98
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.43
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.51
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.80
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.20
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.12
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.13
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.03
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.86
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.64
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.90
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.17
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5116.47
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.46
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.70
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.48
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:28.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.95
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :    1.80
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:24.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.45e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.70
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.47
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.70
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:02.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:07.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9827.91
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:04:20.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.54
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:52.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.54
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3999.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.66
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11602.36
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11578.16
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:32.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.70
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000177718

Normal statistic for number of bits   :    1.40
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.37
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999924194

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:12.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.60
p-value of test                       :    0.95

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.099
p-value of test                       :    0.54

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:00.53

 All tests were passed




Server wird beendet - Lösche Semaphor 104988674.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1462
p-value of test                       :  4.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334582
  j =  1                              :        599997076
  j =  2                              :             1462
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5426
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:52.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:38.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:35.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4560
p-value of test                       :  4.0e-4    *****


-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:02.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:03.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:53.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:00.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    3.20
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     668
p-value of test                       :  3.3e-3

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:14.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:40.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.16
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.37
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.54
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.23
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.23
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.89
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.22
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7043.27
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:01.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.93
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.95
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5026.68
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:00.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45952
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869952
  j =  1                              :        399908100
  j =  2                              :            45944
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45942
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869942
  j =  1                              :        399908121
  j =  2                              :            45932
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  1.9e-3

Anderson-Darling statistic = A2       :    3.75
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.64
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:27.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:18.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:54.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.83e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.75e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:26.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:35.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:38.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.47
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:47.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.68
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:48.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.80
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.47
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.88
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.85
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17539.69
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   14.71
p-value of test                       :    0.9994    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.83
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.27
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.42
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.23
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.38
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.49
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.95
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.89
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.91
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.05
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.58
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.24
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.17
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.23
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.61
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.34
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.90
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.78
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.30
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.05
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5098.34
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.39
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.53
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.93
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.02
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.74
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.66
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.22
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.22
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:25.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.48
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -1.64
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:25.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.99
p-value of test                       :    0.98

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.19e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.13
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.05
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   40.00
p-value of test                       :  4.5e-3



-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.68
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:08.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.99
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10090.72
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:41.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4957.61
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.77
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4197.49
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12019.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11733.26
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.88
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999888332

Normal statistic for number of bits   :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   84.54
p-value of test                       :  5.0e-3


-----------------------------------------------
Total number of bits:  7999813518

Normal statistic for number of bits   :   -1.47
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  1.9e-3

Anderson-Darling statistic = A2       :    5.09
p-value of test                       :  2.8e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.89
p-value of test                       :  2.0e-3

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:11.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 17  BirthdaySpacings, t = 7         4.0e-4
 74  RandomWalk1 H (L=50, r=0)       0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 106135554.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1476
p-value of test                       :  1.5e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334596
  j =  1                              :        599997048
  j =  2                              :             1476
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5562
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:53.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4205
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:38.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:55.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4225
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:02.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:02.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:52.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:58.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     948
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    3.48
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:12.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.87
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.80
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.31
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.89
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.14
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.88
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.93
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.05
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7176.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:41.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.21
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:02.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.44
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.53
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5106.02
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:53.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46230
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870230
  j =  1                              :        399907542
  j =  2                              :            46226
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45818
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869818
  j =  1                              :        399908367
  j =  2                              :            45812
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:27.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:19.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:00.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:32.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:34.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   37.52
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:00:47.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.62
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:47.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.36
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.02
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.33
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.46
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.66
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.39
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  163.41
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17344.99
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.73
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.16
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.74
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.38
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.24
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.61
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.20
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.25
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.38
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.60
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.16
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.81
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.01
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.94
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  190.92
p-value of test                       :  7.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.57
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.69
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.37
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.26
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.40
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.23
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.93
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.91
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.03
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.09
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.58
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.85
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.39
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.61
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:24.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.98
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:24.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.47e-4
p-value of test                       :    0.9994    *****

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.54
p-value of test                       :  5.6e-3

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.35
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.19
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.59
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:05.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:06.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10089.19
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9945

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10024.84
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:41.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.90
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.13
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:51.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4204.16
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4003.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12050.37
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11693.79
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.52
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000020848

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.39
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999940565

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    3.12
p-value of test                       :  9.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:41.32

 All tests were passed




Server wird beendet - Lösche Semaphor 107020290.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5413
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:58.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:43.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:59.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:00.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:10.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7473
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:09.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:06.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:12.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     954
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    2.01
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.02
p-value of test                       :  8.9e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    2.01
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:13.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.96
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:41.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.41
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.47
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.45
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.75
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.01
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.48
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.92
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1343.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:11.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7041.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:57.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.97
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.49
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:13.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.19
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.26
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:41.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5197.50
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:10.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45975
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869975
  j =  1                              :        399908053
  j =  2                              :            45969
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45648
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869648
  j =  1                              :        399908710
  j =  2                              :            45636
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:29.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:24.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:09.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:57.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.063
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:54.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:57.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.80
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.50
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.74
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:53.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.44
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.67
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17534.62
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.51
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.65
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.68
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.73
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.99
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.00
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.31
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.82
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.56
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.05
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.32
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.14
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.30
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.17
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.65
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.21
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.25
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.10
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.23
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.01
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.44
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.57
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.20
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.40
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.54
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.24
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:24.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.79
p-value of test                       :    0.04

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 8.89e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.17e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.11
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.88
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.13
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:29.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.66
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:30.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9891.92
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10126.52
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.98
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.79
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:04:39.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.12
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11584.08
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:33.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11879.30
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:35.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.29
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000009793

Normal statistic for number of bits   :   0.077
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.92
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999837365

Normal statistic for number of bits   :   -1.29
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   0.075
p-value of test                       :    0.47

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:32.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:30.95

 All tests were passed




Server wird beendet - Lösche Semaphor 107937794.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5467
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:54.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:40.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:05.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:04.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:54.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:00.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.07
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    2.96
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:13.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:45.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.48
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.57
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.12
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.87
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.10
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.56
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.07
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.31
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.69
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.06
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7006.19
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.46
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.21
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:04.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.01
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.65
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:32.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5104.27
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:57.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46017
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870017
  j =  1                              :        399907969
  j =  2                              :            46011
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46134
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870134
  j =  1                              :        399907739
  j =  2                              :            46120
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:25.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:46.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:32.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.72e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 8.97e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.66e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 9.25e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:37.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:38.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.52
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.05
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.72
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.07
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.33
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.85
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.43
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.34
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17275.82
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.24
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.41
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.62
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.39
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.40
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.00
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.89
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.47
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.38
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.07
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.21
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.52
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.36
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.23
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.16
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.07
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.82
p-value of test                       :  8.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.31
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  101.00
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.73
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.39
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.71
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.50
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.56
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.46
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.35
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.64
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4878.02
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.54
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.52
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.45
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:23.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.15
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.17e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 5.16e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.75
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.72
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.49
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:04.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.91
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:05.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10106.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9880.47
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:47.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.76
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.73
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.49
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4048.93
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.96
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11984.43
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.36
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999973235

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.66
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999854948

Normal statistic for number of bits   :   -1.15
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         : -8.32e-3
p-value of test                       :    0.50

Sample variance                       :    2.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.38e-4
p-value of test                       :    0.9997    *****

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    2.13
p-value of test                       :    0.02

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:15.11

 All tests were passed




Server wird beendet - Lösche Semaphor 109346818.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5436
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:53.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:05.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:04.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:55.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:01.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.48
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.52
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:13.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:43.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.79
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.92
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    4.98
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.50
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.87
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.86
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1506.37
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:02.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7260.43
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.51e-4
p-value of test                       :    0.9996    *****

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   36.35
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:03:02.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.04
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.89
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:35.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5129.20
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45649
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869649
  j =  1                              :        399908704
  j =  2                              :            45645
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46176
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870176
  j =  1                              :        399907650
  j =  2                              :            46172
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:25.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:17.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:01.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.71e-3
p-value of test                       :    0.9924

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 8.01e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -3.02e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:37.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:35.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.33
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.20
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.50
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.77
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.33
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.03
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.13
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.76
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17469.01
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.44
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.30
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.42
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.98
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.63
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.50
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.31
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.28
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.98
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.15
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.96
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.21
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  428.58
p-value of test                       :    0.9907


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.97
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.74
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.89
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.69
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  437.05
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.18
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.76
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.60
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5122.93
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.73
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.77
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.42
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.56
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.87
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  315.13
p-value of test                       :    0.9919


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.17
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.30
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -1.21
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:22.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.28
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:23.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   0.098
p-value of test                       :    0.46

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 3.21e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.12e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 6.85e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.08
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.36
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.55
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:05.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:05.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9827.69
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.03
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.084
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:45.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.56
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.90
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3984.53
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11818.86
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11619.43
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.91
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000009040

Normal statistic for number of bits   :   0.071
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.22
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000014290

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9934

Tests on the sum of all N observations
Standardized normal statistic         :  -0.034
p-value of test                       :    0.51

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         : 8.64e-3
p-value of test                       :    0.50

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.50
p-value of test                       :    0.93

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:28.18

 All tests were passed




Server wird beendet - Lösche Semaphor 110362626.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5365
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:57.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:42.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:01.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:01.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7118
p-value of test                       :    0.9905


-----------------------------------------------
CPU time used                    :  00:03:15.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:13.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:13.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:15.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    2.15
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.40
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:15.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:44.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.71
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.48
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.10
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.56
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.40
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.45
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:06.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.63
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:32.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6998.27
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:04.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.32
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:15.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.91
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.06
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:38.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5048.72
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45501
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869501
  j =  1                              :        399909000
  j =  2                              :            45497
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45660
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869660
  j =  1                              :        399908681
  j =  2                              :            45658
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:31.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:23.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:55.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:12.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:02.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:46.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.70e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 9.64e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.76e-6
p-value of test                       :    0.9982

Kolmogorov-Smirnov- statistic = D-    : 3.84e-4
p-value of test                       :  2.8e-3

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.014
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:51.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:50.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.63
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.07
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.13
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.31
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   60.72
p-value of test                       :  5.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.61
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   18.35
p-value of test                       :  3.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  1.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.69
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17351.18
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.23
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.54
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.03
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.65
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.86
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.92
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.62
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.24
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.69
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.70
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.76
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.38
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.19
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.28
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  568.02
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.71
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.18
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.89
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.71
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.41
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.71
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.40
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.81
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.22
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.22
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:23.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.38
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:23.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.66e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:47.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.87e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.04
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.08
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.35
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:10.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.97
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:11.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.09
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9886.28
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:11.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:04:28.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5011.92
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:58.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.09
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.34
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.03
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11512.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12072.30
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:34.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.55
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999823559

Normal statistic for number of bits   :   -1.39
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.09
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999843989

Normal statistic for number of bits   :   -1.23
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.35
p-value of test                       :    0.9905

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:04.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 65  SumCollector                    5.0e-4
 68  MatrixRank, L=1000, r=0         3.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 111345674.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:55.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4452
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:04.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:04.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:56.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:01.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    4.98
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.92
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    2.15
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     640
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:14.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:44.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.09
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.12
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.22
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.14
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.73
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.17
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.50
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7290.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.21
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.96
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:06.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.07
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.14
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4919.33
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:02.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45536
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869536
  j =  1                              :        399908931
  j =  2                              :            45530
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46248
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870248
  j =  1                              :        399907510
  j =  2                              :            46236
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:27.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:45.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:58.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:54.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.77e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.93e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:37.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.61
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.50
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.50
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:37.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.88
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.55
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.10
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9960

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17401.34
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.51
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   44.38
p-value of test                       :  9.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.15
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   36.25
p-value of test                       :  4.2e-3


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.05
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.17
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.52
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.01
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.89
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.50
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.60
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.89
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.60
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.05
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.51
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.45
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.44
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.16
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.65
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.32
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.46
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.60
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.81
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.57
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.17
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.05
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.14
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.63
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.37
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.53
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:25.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.97
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:24.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 3.41e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.77e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 8.34e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.10
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.23
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.12
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:04.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.61
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:05.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9720.71
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.16
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:42.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.06
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.18
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.07
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.03
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11712.16
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:29.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.48
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999948914

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.93
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000054061

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.96
p-value of test                       :    0.02

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:24.62

 All tests were passed




Server wird beendet - Lösche Semaphor 112361482.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5368
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:57.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4214
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:44.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:10.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:11.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:04:08.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:15.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    2.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:14.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.00
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:45.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.63
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.06
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.71
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  188.34
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.32
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:09.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7091.16
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.08
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:19.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.24
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.09
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:43.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5017.32
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:57.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45586
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869586
  j =  1                              :        399908833
  j =  2                              :            45576
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45730
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869730
  j =  1                              :        399908545
  j =  2                              :            45720
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:31.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:21.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:52.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:10.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:57.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.53e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:50.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   97.97
p-value of test                       :  8.1e-3

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.76
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.85
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.49
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.63
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.10
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.99e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   63.82
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.84
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17066.80
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.06
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.59
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.83
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.97
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.85
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.89
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.56
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.79
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.76
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.14
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.64
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.15
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.73
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.76
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.67
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  570.89
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.12
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.07
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.76
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.18
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.29
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.72
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.32
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.31
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.70
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.63
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.80
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.16
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.86
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :    1.38
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:25.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.79
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:25.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 4.08e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.75
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.27
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.91
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:06.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:04.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.06
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9891.48
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:04:25.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.47
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:00.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11999.51
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:37.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.16
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999970151

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.45
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999900050

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:07.48

 All tests were passed




Server wird beendet - Lösche Semaphor 113377290.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:52.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:40.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:04.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7122
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:05.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:55.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:02.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.24
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     271
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:13.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:45.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.10
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.80
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.99
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.71
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.83
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.90
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1507.49
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:03.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6948.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.14
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:02.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.19
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.61
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4930.61
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:59.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46048
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870048
  j =  1                              :        399907905
  j =  2                              :            46046
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45595
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869595
  j =  1                              :        399908811
  j =  2                              :            45593
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:27.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  1.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:17.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:55.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:35.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:37.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:37.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.41
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.74
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.06
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.14
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.61
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.32
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.93
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17356.79
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.38
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.46
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.64
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.97
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.35
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.40
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.45
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.91
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.56
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.57
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.98
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.29
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.04
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.51
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.78
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.15
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.99
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.31
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.62
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.76
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.83
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.29
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.93
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.51
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.68
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.86
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.51
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.25
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.41
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:25.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.95
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    1.67
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:24.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.91e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 3.56e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.74
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.95
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.04
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:10.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.43
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.74
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10127.28
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:36.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.10
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5012.52
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.01
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4258.16
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11616.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11830.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.25
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999970940

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.80
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000057466

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:15.29

 All tests were passed




Server wird beendet - Lösche Semaphor 114524170.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5357
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:53.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:40.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7472
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:04.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:05.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:55.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:02.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.54
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:14.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.13
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    2.49
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     182
p-value of test                       :  6.2e-3

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:39.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.87
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.39
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.30
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.34
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.67
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.46
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.52
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:43.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1355.27
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:01.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6879.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.13
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:03.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.55
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.83
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:35.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.54
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:02.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45961
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869961
  j =  1                              :        399908086
  j =  2                              :            45945
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46093
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870093
  j =  1                              :        399907816
  j =  2                              :            46089
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:28.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:18.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:34.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.31e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:36.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:37.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.79
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.87
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.58
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.46
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.75
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.30
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.02
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17202.61
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.12
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.03
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.41
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.75
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.52
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.75
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.89
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.38
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.93
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.87
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.77
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.35
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.97
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.54
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.13
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.67
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.59
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.85
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.09
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.57
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.71
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.77
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.64
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.91
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.07
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.16
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.52
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.99
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.22
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    1.89
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:25.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.00
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:25.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.25
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.12
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.66
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:04.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.45
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:02.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9963.67
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9873.63
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:37.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.55
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.00
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:50.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.07
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12006.05
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11701.02
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.44
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000183991

Normal statistic for number of bits   :    1.45
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.93
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999896144

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:11.10

 All tests were passed




Server wird beendet - Lösche Semaphor 115507210.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:54.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:04.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:55.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7490
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:02.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:13.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.97
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     126
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:43.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.71
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.77
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.15
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.98
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.12
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.59
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.47
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:44.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.54
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:00.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7147.38
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.46
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:03.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.16
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.66
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4930.19
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:00.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45756
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869756
  j =  1                              :        399908492
  j =  2                              :            45748
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45839
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869839
  j =  1                              :        399908327
  j =  2                              :            45829
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:27.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:19.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:58.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:01:55.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:35.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.87e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.31e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 3.12e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:37.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.059
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.12
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.25
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.12
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.58
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:48.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.94
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.19
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.21
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.57
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17474.68
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.51
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.57
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   45.84
p-value of test                       :  6.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.55
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.08
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.79
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.49
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.25
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.68
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.90
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.88
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.65
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.16
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  184.63
p-value of test                       :  3.5e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.77
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.96
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.04
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.88
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.46
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.69
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.75
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.89
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5183.69
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.49
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.45
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.71
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.99
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.88
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.18
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.77
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.34
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    1.82
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:23.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.83
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    1.22
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:23.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.69e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.68
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.25
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:02.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:03.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9836.95
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10024.65
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:39.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.18
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:47.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.10
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.42
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11400.05
p-value of test                       :    0.9974

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11873.67
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.88
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000040645

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.54
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999792284

Normal statistic for number of bits   :   -1.64
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:56.93

 All tests were passed




Server wird beendet - Lösche Semaphor 116457482.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5471
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:55.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:43.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4198
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:00.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:11.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:11.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:10.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:15.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    2.40
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9938

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    2.23
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     647
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:14.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.45
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.48
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.79
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.50
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.44
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.56
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.90
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:33.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.13
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:00.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1358.91
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:10.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7350.55
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.40
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:20.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.02
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.87
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5030.38
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:59.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45888
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869888
  j =  1                              :        399908232
  j =  2                              :            45872
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46116
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870116
  j =  1                              :        399907771
  j =  2                              :            46110
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:31.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:21.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:52.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:10.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 8.95e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.096
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:50.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.88
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.93
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.36
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.43
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:53.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
p-value of test                       :    0.9998    *****

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   66.05
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.66
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17428.20
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.18
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.05
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.10
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.79
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.36
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.84
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.55
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.00
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.64
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.29
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.26
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.31
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.76
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.73
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.84
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.02
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.85
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.48
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.00
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.28
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.42
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.88
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.76
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.71
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.57
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.87
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5114.23
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.92
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.22
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.84
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:23.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.21
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:22.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.63e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.40e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.55
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.51
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.59
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:06.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.93
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:07.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9841.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10133.86
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:04:26.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5023.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4781.19
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4277.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.81
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.23
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.59
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:38.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.60
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999995804

Normal statistic for number of bits   :  -0.033
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.32
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999927359

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.04
p-value of test                       :    0.98

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    2.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:56.63

 All tests were passed




Server wird beendet - Lösche Semaphor 117473290.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5461
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7472
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:44.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:02.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:11.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:11.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:08.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:12.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    2.07
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:13.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.55
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:41.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.01
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.35
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.41
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.94
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.37
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.44
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.44
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.44
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1356.03
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:07.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6860.08
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:58.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.18
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.73
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:16.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.67
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.19
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4961.02
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:00.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45731
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869731
  j =  1                              :        399908542
  j =  2                              :            45723
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45971
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869971
  j =  1                              :        399908061
  j =  2                              :            45965
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:32.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:23.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:09.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.09e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.81e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.91
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.38
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.24
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.53
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.10
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.10
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.81
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17442.57
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.43
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.71
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    4.68
p-value of test                       :    0.9985


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.20
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.82
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.16
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.43
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.30
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.26
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.61
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.64
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  109.99
p-value of test                       :  4.2e-3


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.59
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.00
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.34
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.24
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.55
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.32
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.74
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.02
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.64
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.03
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.36
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.62
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.24
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.45
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.76
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:21.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.10
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:20.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 2.16e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.19
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.42
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.94
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.58
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:05.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9934

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10014.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.056
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:04:23.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:56.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5067.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.90
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4224.41
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11596.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:35.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11907.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:38.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.28
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999979949

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.06
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000089644

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:44.68

 All tests were passed




Server wird beendet - Lösche Semaphor 118685706.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:50.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5344
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:54.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:04.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:56.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:01.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.34
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     850
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.57
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    2.63
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:16.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:47.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.90
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.53
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.61
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.75
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.04
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.32
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.66
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  391.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1502.31
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7045.79
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:41.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.85
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:01.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.90
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.10
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:32.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4929.25
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:00.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45573
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869573
  j =  1                              :        399908859
  j =  2                              :            45563
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46102
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870102
  j =  1                              :        399907803
  j =  2                              :            46088
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.54e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:28.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:00.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:55.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.93e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 3.38e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.69e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.50
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.25
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.58
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.39
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.71
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.80
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.55
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.49
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17128.14
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.23
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.41
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.50
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.11
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.94
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.16
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.44
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.93
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.87
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.14
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.52
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.26
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.76
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.30
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.40
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.22
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.65
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.78
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.17
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.70
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.71
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.46
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5153.61
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.65
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.94
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.73
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.19
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.77
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.11
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.19
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.63
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:21.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.28
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    1.59
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:20.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.46e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 9.75e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.56
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.42
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:03.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:03.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10186.94
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10145.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:38.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.35
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:47.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.35
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.88
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.38
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11972.63
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11716.29
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.89
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999855566

Normal statistic for number of bits   :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.78
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000101176

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.69
p-value of test                       :    0.05

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:06.69

 All tests were passed




Server wird beendet - Lösche Semaphor 119799818.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:55.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:45.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:10.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7174
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:10.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:58.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:05.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:14.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.29
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    4.03
p-value of test                       :  8.5e-3

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:44.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.28
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.15
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.39
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.36
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.14
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.54
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.55
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.20
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:43.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:20.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7170.31
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.62
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.94
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:02.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.90
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.56
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:35.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4973.85
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:00.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45756
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869756
  j =  1                              :        399908492
  j =  2                              :            45748
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45825
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869825
  j =  1                              :        399908351
  j =  2                              :            45823
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:29.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:20.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :  3.0e-3

Anderson-Darling statistic = A2       :    3.50
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 8.59e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:02.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:57.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 9.29e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 8.89e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.022
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:34.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.00
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.59
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:39.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.15
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.17
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.00
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17439.23
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.61
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.66
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.38
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.53
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.19
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.64
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.70
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.41
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.06
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.94
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.62
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.64
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.96
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.26
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.33
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.85
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.22
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.50
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.77
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.36
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.60
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.86
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.06
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.51
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.87
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.70
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.40
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.43
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.60
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.69
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:21.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.80
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :  -0.019
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:20.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.12

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 7.99e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.52e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.87
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.91
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.37
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:05.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.30
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:04.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10271.12
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:39.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5004.10
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4759.02
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4223.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.42
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12004.90
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.12
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999931214

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.68
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000063265

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.1e-3

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.23
p-value of test                       :    0.01

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:24.45

 All tests were passed




Server wird beendet - Lösche Semaphor 120750090.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5314
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:56.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:05.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:55.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:02.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     643
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    2.28
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:14.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:44.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.67
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.42
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.66
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.35
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:44.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1522.16
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:02.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7189.51
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.01
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.22
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:01.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.35
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.78
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:45.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5206.81
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:31.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:22.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46060
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870060
  j =  1                              :        399907885
  j =  2                              :            46050
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45810
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869810
  j =  1                              :        399908385
  j =  2                              :            45800
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:27.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:17.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:46.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:02.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:34.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.87e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.62
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.14
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.31
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.52
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.81
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.15
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.52
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.15
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.46
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17293.23
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.47
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.02
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.16
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.52
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.51
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.17
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.79
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.82
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.38
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.04
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.35
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.91
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.95
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.67
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.53
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.06
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.01
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.16
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  186.87
p-value of test                       :  2.5e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.59
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.72
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.24
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.67
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.81
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.27
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.97
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.76
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.26
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.13
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.79
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.90
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:11.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.15
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :   0.083
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:11.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.74e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 9.61e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 6.02e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:40.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.97
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.76
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.29
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:54.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10105.52
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:17.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.28
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.09e-3
p-value of test                       :    0.9968

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5061.08
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3966.82
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.39
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11962.08
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11754.76
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.23
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999936371

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.45
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999980069

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:15.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:58:12.77

 All tests were passed




Server wird beendet - Lösche Semaphor 121733130.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:47.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5427
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:40.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:33.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:54.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:54.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:01.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:01.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:52.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:57.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.49
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:51.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.53
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    2.61
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     554
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.63
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:09.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:35.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.38
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.57
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.57
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.34
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.85
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:51.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1322.62
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:02.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7278.45
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:51.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.00
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:02.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.91
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.18
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5082.90
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:13.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45866
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869866
  j =  1                              :        399908274
  j =  2                              :            45854
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45913
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869913
  j =  1                              :        399908181
  j =  2                              :            45899
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:27.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:16.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:43.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:58.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:51.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 8.19e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.31e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.021
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.33
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.61
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.20
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.65
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.62
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:42.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.21
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:32.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.69
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17195.73
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.70
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.13
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.94
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.22
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.43
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.15
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.85
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.35
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.02
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.68
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.19
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.16
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.63
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.88
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.63
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.69
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.13
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.60
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.59
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.04
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.24
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.93
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.81
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.46
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.38
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.65
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.26
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4775.80
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.94
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.37
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.46
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:13.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.25
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:12.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.02e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 8.39e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:47.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.21e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.93
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.41
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.25
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:09.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.52
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:10.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.97
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:45.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.9e-3

Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
p-value of test                       :    0.9921

Anderson-Darling statistic = A2       :    3.65
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4628.46
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:01:47.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.64
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.00
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4258.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12003.41
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11963.35
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.98
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000055357

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.79
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999944531

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   0.096
p-value of test                       :    0.46

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:14:35.93

 All tests were passed




Server wird beendet - Lösche Semaphor 101679107.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:56.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1221
p-value of test                       : 1 -  4.2e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334341
  j =  1                              :        599997558
  j =  2                              :             1221
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5343
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:42.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:33.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:52.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:00.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7542
p-value of test                       :  4.7e-3


-----------------------------------------------
CPU time used                    :  00:03:02.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:54.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:58.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     269
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:10.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.64
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     125
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:45.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.63
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.40
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.25
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.18
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  271.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.95
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.18
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:06.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6980.45
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.13
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:08.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.06
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.26
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4990.71
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:18.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46244
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870244
  j =  1                              :        399907513
  j =  2                              :            46242
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45952
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869952
  j =  1                              :        399908101
  j =  2                              :            45942
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:28.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :  1.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    4.04
p-value of test                       :  8.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:17.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:59.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:53.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 5.35e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.92
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.73
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.07
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.85
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.13
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.58
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.02
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:33.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.64
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17458.47
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:50.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.50
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.56
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.97
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.85
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.89
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.19
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.09
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.95
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.65
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.34
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.87
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.94
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.94
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.47
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.68
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.54
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.69
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.18
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.98
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.73
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.57
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.51
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.66
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.00
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.20
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.98
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.83
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.05
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  246.67
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.00
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:25.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.11
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   0.061
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:22.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.95e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.04
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.26
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:08.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.68
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:09.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.30
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.31
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:04:16.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.51
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:51.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5000.24
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:53.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.77
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11871.74
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11713.60
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:32.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.33
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000030349

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.44
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999807713

Normal statistic for number of bits   :   -1.52
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :  -0.079
p-value of test                       :    0.53

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:43.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21          1 -  4.2e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 103284739.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5356
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:45.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:35.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:54.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:55.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7097
p-value of test                       :    0.9952


-----------------------------------------------
CPU time used                    :  00:03:02.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:02.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:52.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:57.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.75
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:16.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.56
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.64
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.26
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.00
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  270.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.12
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:00.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7201.44
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:41.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:02.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.18
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   88.10
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4851.70
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:04.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45932
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869932
  j =  1                              :        399908139
  j =  2                              :            45926
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45851
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869851
  j =  1                              :        399908300
  j =  2                              :            45847
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:27.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:17.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:44.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:54.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:33.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.44e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.034
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:35.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.25
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.87
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.11
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.45
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.85
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.27
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.64
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.31
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 4.66e-3
p-value of test                       :    0.9951

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17822.64
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.59
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.39
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.41
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.88
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.28
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.36
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.70
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.25
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.56
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.49
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.38
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.00
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.59
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.71
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.67
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.92
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.76
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.95
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.39
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.83
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.93
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.73
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.81
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.42
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.12
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.51
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5109.76
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.69
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.41
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.61
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:24.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.14
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:27.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.15e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.89e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 4.95e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.42
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.49
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.84
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:06.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.75
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:08.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  2.9e-3

Anderson-Darling statistic = A2       :    4.90
p-value of test                       :  3.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10348.91
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:39.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.45
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:50.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4224.42
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.61
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.86
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.00
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000119230

Normal statistic for number of bits   :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.26
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000060088

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:00.79

 All tests were passed




Server wird beendet - Lösche Semaphor 104366083.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1233
p-value of test                       :    0.9998    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334353
  j =  1                              :        599997534
  j =  2                              :             1233
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5419
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:49.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:38.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:37.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4439
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:01.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:02.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:52.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:58.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    2.11
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9943

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:13.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:44.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.14
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.58
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.17
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.64
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.33
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.38
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.19
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.19
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.60
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7135.01
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:02.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.02
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.06
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4957.56
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45746
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869746
  j =  1                              :        399908511
  j =  2                              :            45740
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46071
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870071
  j =  1                              :        399907863
  j =  2                              :            46061
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:27.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.93e-3
p-value of test                       :    0.9958

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  9.9e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:59.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:53.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:32.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.66e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:33.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:48.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.43
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.81
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.39
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.93
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17765.71
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.90
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.44
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.64
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.43
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.29
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.28
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.15
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.94
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.10
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.75
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.72
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.27
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.41
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.75
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.19
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.51
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.21
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.54
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.01
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.54
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.93
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.14
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.44
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.51
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.29
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.23
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.47
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.50
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.38
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.81
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:23.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   0.060
p-value of test                       :    0.48

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 6.12e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.31e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 6.10e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.99
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.91
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:04.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.62
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  152.76
p-value of test                       :    0.9945

-----------------------------------------------
CPU time used                    :  00:02:07.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9818.70
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.06
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.027
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:43.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5039.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5028.78
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4232.71
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12063.67
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12003.05
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:29.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.37
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000026134

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   31.72
p-value of test                       :    0.9933


-----------------------------------------------
Total number of bits:  7999892745

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.58e-3
p-value of test                       :    0.9941

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.87
p-value of test                       :    0.97

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:59.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14           0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 105218051.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:40.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5463
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:52.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4224
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:35.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:53.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:55.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:02.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:03.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:53.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:58.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.04
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:15.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:44.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.93
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.02
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.28
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.23
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.68
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.35
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.96
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.93
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.42
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.59
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:06.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7325.99
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.43
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.01
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:09.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.03
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.90
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:36.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5321.71
p-value of test                       :  2.8e-3


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:15.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45838
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869838
  j =  1                              :        399908325
  j =  2                              :            45836
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45935
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869935
  j =  1                              :        399908133
  j =  2                              :            45929
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:29.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:18.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:45.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:02.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:56.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.49e-6
p-value of test                       :    0.9978

Kolmogorov-Smirnov- statistic = D-    : 2.95e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.81e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.044
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.096
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.38
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.73
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.65
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.89
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.98
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.57
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17250.17
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.81
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.29
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.01
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.27
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.16
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.13
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.00
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.85
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.77
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.32
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.31
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.39
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.02
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.03
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.93
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.52
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.20
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.34
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.11
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.44
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.53
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.76
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  155.57
p-value of test                       :    0.9913


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.71
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.20
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.64
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.48
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.80
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.15
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    1.78
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:21.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.63
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:20.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 6.48e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.69e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 8.90e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.52
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.89
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.16
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:04.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10108.09
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9952.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:04:16.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5032.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:52.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11903.89
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.74
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:30.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.21
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999953729

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.91
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000074650

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    0.21
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:18.43

 All tests were passed




Server wird beendet - Lösche Semaphor 106070019.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5399
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:48.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:38.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4461
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:55.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:01.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:01.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:54.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:58.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:14.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.97
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.54
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.98
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.14
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.87
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.64
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.16
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.90
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1406.98
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6827.08
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.38
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:04.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.77
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.53
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:35.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5084.35
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:02.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45813
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869813
  j =  1                              :        399908377
  j =  2                              :            45807
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45973
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869973
  j =  1                              :        399908056
  j =  2                              :            45969
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:27.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:20.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:01.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:55.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 8.29e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:38.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:38.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.40
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.72
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.83
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.45
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.35
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.03
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17214.26
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.20
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.56
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.80
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.87
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.56
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.02
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.66
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.80
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.31
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.02
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.80
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.52
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.06
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.73
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.29
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.32
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.13
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.10
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.40
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.80
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.26
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.06
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.89
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.30
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.44
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.15
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.27
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.63
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.78
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.50
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.63
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    1.98
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:24.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.08
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -1.15
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:25.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.74e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.47
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.78
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:05.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.56
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:06.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.79
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.49
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:12.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.63
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:50.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.05
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.19
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.98
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11922.17
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:30.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.19
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999969218

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.42
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999972005

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    2.70
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:18.20

 All tests were passed




Server wird beendet - Lösche Semaphor 107216899.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5481
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:53.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:38.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4463
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:02.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:02.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:53.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:58.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.72
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     943
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    2.07
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    3.36
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:13.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:40.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.96
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.98
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.28
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.02
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.69
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  388.74
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7090.16
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:45.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.34
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.73
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:04.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.34
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.30
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4905.18
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:59.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45295
p-value of test                       :    0.9968


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869295
  j =  1                              :        399909414
  j =  2                              :            45287
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46093
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870093
  j =  1                              :        399907820
  j =  2                              :            46081
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:28.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:19.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:45.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:55.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:32.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 9.17e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -3.03
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.073
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:38.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.50
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.52
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:47.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   12.03
p-value of test                       :    0.9977

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.55
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.39
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17252.93
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.85
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.97
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.59
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.71
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.75
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.20
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.27
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.87
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.91
p-value of test                       :    0.9949


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.77
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.65
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.91
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.29
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.90
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.94
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.22
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.55
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.05
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.36
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.71
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.72
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.51
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.22
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.51
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.06
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.32
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4853.31
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.41
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.76
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.68
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -1.57
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:24.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.01
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :   -1.23
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:24.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 4.28e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.83
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.78
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.60
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:05.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.18
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:05.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10024.12
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9818.42
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:53.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.82
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:49.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.62
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12327.53
p-value of test                       :  6.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.11
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.47
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000029077

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.83
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999968417

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :  -0.089
p-value of test                       :    0.54

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.16
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.86
p-value of test                       :    0.03

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:36.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 99  HammingIndep, L=1200, r=0       6.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 108167171.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5470
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:53.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:39.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:58.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:05.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:05.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:59.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:00.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.30
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.41
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:13.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.76
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.62
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.90
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.05
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  381.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1497.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:03.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7209.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.08
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:08.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.45
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  159.63
p-value of test                       :  7.7e-3


-----------------------------------------------
CPU time used                    :  00:01:37.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5224.27
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:57.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45649
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869649
  j =  1                              :        399908706
  j =  2                              :            45641
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45987
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869987
  j =  1                              :        399908027
  j =  2                              :            45985
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:29.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:18.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:36.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.94e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 2.91e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.34e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.81e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.82
p-value of test                       :    0.9976

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:37.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.47
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.40
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.01
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.81
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.41
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.10
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.94
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.48
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17232.73
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.66
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.71
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.53
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.42
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.37
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.19
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.17
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.98
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.16
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.89
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  434.57
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.50
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.40
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.77
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.04
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.03
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.24
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.32
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.90
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.63
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.27
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.48
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.15
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.80
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.72
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5094.12
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  433.80
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.01
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.82
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:26.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.21
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :   -1.52
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:25.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.25
p-value of test                       :    0.99

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.98e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.36e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.26
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.22
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.91
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:07.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10043.34
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:04:14.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:53.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:56.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.76
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12122.18
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:30.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.50
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.67
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999977297

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.90
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999950978

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.34

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:57.35

 All tests were passed




Server wird beendet - Lösche Semaphor 109150211.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5515
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:52.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:09.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:07.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7097
p-value of test                       :    0.9952


-----------------------------------------------
CPU time used                    :  00:04:05.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:08.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.95
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:11.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:39.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.61
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.79
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.38
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  273.65
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.56
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.26
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:07.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7125.84
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 9.71e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.42
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.56
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:15.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.11
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.07
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5286.55
p-value of test                       :  7.5e-3


-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:57.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45985
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869985
  j =  1                              :        399908038
  j =  2                              :            45969
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45982
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869982
  j =  1                              :        399908040
  j =  2                              :            45974
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:30.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:19.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:06.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.68e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.065
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:53.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.77
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.98
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.55
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:50.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9938

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.82
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.02
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.65
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17633.43
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.35
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.09
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.31
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   37.47
p-value of test                       :  2.9e-3


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.99
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.57
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.72
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.00
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.09
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.87
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.05
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.66
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   47.33
p-value of test                       :    0.9933


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.81
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.78
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.47
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.14
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.14
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.75
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4882.53
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.75
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.84
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.95
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.62
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4885.86
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.63
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.61
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.24
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.87
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.30e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 9.70e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.49e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.10
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.11
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.68
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:06.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.04
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:05.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.69
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10274.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:04:27.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5030.50
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.98
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.39
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.70
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11889.33
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:33.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.80
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999934307

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.50
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000119887

Normal statistic for number of bits   :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.65e-3
p-value of test                       :    0.9918

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.39
p-value of test                       :  8.4e-3

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:56.72

 All tests were passed




Server wird beendet - Lösche Semaphor 110231555.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5451
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:52.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:40.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:04.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:54.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:00.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:13.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:43.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.74
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   19.33
p-value of test                       :  7.2e-3

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.74
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.58
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.12
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.16
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.68
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:43.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7180.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.53
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:06.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.81
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  155.41
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4950.07
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:03.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46048
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870048
  j =  1                              :        399907906
  j =  2                              :            46044
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45308
p-value of test                       :    0.9962


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869308
  j =  1                              :        399909391
  j =  2                              :            45294
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  7.9e-3

Kolmogorov-Smirnov- statistic = D-    : 1.70e-3
p-value of test                       :    0.9982

Anderson-Darling statistic = A2       :    3.83
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.52e-4
p-value of test                       :    0.9992    *****

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:45.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.01e-4
p-value of test                       :    0.9993    *****

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:01.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 8.55e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:33.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.00e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 7.33e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    3.23
p-value of test                       :  6.1e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.041
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:34.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.46
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.45
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.10
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.92
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:39.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.66
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.42
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.22
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
p-value of test                       :    0.9997    *****

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.48
p-value of test                       :  5.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :18043.45
p-value of test                       :  5.7e-4    *****



-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.78
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.88
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.65
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.55
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.50
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.68
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.36
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.91
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.56
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.18
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.75
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.98
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.70
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.69
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.64
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.40
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.43
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.28
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.94
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.51
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.80
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5088.67
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  432.81
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  257.60
p-value of test                       :  3.7e-3


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.98
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.13
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.71
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.76
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.08
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.32
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.85
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    2.03
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:26.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.41e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.64
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.35
p-value of test                       :    0.9949

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:07.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.16
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:05.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10106.93
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10035.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.31
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:40.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4933.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.11
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.10
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11734.24
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11652.25
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.83
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000085117

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.83
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000186331

Normal statistic for number of bits   :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:23.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 57  AppearanceSpacings, r = 0       6.1e-4
 73  GCD                             5.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 111378435.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5348
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:54.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4133
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:04.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:54.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:00.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    2.41
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:14.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:41.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.00
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.27
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.09
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.43
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.72
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.10
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6932.02
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.11
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:05.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.70
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.75
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:30.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5132.27
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:57.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45809
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869809
  j =  1                              :        399908386
  j =  2                              :            45801
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869892
  j =  1                              :        399908218
  j =  2                              :            45888
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.58e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:28.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:19.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:47.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:55.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:35.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-5
p-value of test                       :    0.9914

Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.99e-6
p-value of test                       :    0.9990    *****

Kolmogorov-Smirnov- statistic = D-    : 3.56e-4
p-value of test                       :  6.2e-3

Anderson-Darling statistic = A2       :    5.25
p-value of test                       :  2.2e-3

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.057
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:34.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:34.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.92
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.33
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.42
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.46
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.52
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17642.88
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.97
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.54
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.96
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.53
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.17
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.32
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.30
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.47
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.72
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.58
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.76
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.67
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.12
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.40
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.34
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.06
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.42
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.88
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.34
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.99
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.77
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.61
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5194.35
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.40
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.31
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.74
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.51
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.84
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.30
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.92
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.36
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:24.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.87
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -1.22
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:24.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 6.69e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.97e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 6.22e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.27
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.16
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:06.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.12
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:06.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.32
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9892.53
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.086
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:42.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.52
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.31
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:49.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.27
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11922.07
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11831.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.82
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000056200

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.59
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000132805

Normal statistic for number of bits   :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.85

Sample variance                       :    0.22
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:16.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 17  BirthdaySpacings, t = 7         0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 112295939.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5501
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:52.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:05.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:04.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:54.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:00.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.33
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     271
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:13.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.28
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:43.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.49
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.63
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.81
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.13
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.24
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.49
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.86
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1538.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7020.70
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.97
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.84
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:03.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.67
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.22
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5064.91
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:53.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45962
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869962
  j =  1                              :        399908079
  j =  2                              :            45956
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45711
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869711
  j =  1                              :        399908580
  j =  2                              :            45707
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:26.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:17.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.94e-3
p-value of test                       :    0.9934

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.44e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:31.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:34.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.62
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.63
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.94
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.06
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.99
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.96
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.53
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:38.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.41
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.54
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.97
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.74
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.96
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17471.45
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.08
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   61.78
p-value of test                       :  3.5e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.96
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.32
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.36
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.37
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.02
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.15
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.18
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.67
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.39
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.48
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.80
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.24
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.57
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.41
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.57
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.39
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.30
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.95
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.06
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.57
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.22
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.40
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.09
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4878.40
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.19
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.91
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.48
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:21.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.41
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 9.98e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.08e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.03
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.17
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.84
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9872.64
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9772.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.028
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.18
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:44.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.36
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5033.82
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:49.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4003.88
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3986.01
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11680.72
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12185.06
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.59
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000089782

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.97
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000168211

Normal statistic for number of bits   :    1.33
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:58.68

 All tests were passed




Server wird beendet - Lösche Semaphor 113311747.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9962


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5292
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:56.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:43.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:02.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7113
p-value of test                       :    0.9919


-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:10.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:04.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:05.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    2.16
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:12.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.84
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.49
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.07
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.19
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.56
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  302.14
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.62
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:56.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6929.92
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.71
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.34e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.60
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.69
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.29
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4945.23
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:53.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45412
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869412
  j =  1                              :        399909178
  j =  2                              :            45408
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45985
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869985
  j =  1                              :        399908034
  j =  2                              :            45977
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:30.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:20.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:51.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:09.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:56.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.19e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.39e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 3.34e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.28
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.058
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.21
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.09
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.46
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.96
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.88
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:51.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.27
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.46
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17638.80
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.07
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.84
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.69
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.77
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.91
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.28
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.63
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.48
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.94
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.85
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.31
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.37
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.58
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.09
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.85
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.23
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.41
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.66
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.50
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.56
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.62
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5113.92
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.79
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.34
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.03
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.12
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.53
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.45
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.74
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.18
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.01
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   0.021
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:23.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.40e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 4.38e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.67
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.78
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:05.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.79
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:07.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.77
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:04:21.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4956.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:55.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.21
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.00
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.38
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:34.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.96
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:34.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.25
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000228862

Normal statistic for number of bits   :    1.81
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.24
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000170713

Normal statistic for number of bits   :    1.35
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :  -0.068
p-value of test                       :    0.53

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:48.30

 All tests were passed




Server wird beendet - Lösche Semaphor 114262037.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:57.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:41.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:40.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7512
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:04.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:56.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:01.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     954
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     531
p-value of test                       :    0.9978

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.80
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:14.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.07
p-value of test                       :  8.8e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.60
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    3.79
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.76
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.53
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.77
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.61
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.90
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.47
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.77
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.46
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:00.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7074.70
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.76
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:06.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.24
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   81.15
p-value of test                       :    0.9968


-----------------------------------------------
CPU time used                    :  00:01:29.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5057.98
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9994    *****


-----------------------------------------------
CPU time used                    :  00:02:55.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45487
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869487
  j =  1                              :        399909026
  j =  2                              :            45487
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45697
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869697
  j =  1                              :        399908612
  j =  2                              :            45685
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:28.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:18.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:35.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.22e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.43
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.061
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:33.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.18
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.73
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.73
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.74
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.51
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.17
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:37.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.51
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.79
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17567.61
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.70
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.99
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.48
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.60
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.50
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.12
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.16
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.54
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.54
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.01
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.13
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.87
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.64
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.21
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.86
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.41
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.76
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.24
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.98
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.33
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.30
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4895.17
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.76
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.25
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.54
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.26
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.92
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  245.93
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.35
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.10
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:25.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.36e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.97e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 9.89e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.69
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.83
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.95
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:05.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.98
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:06.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.61
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.54
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:39.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4722.40
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.98
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4194.04
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11928.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11730.10
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:30.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.11
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000037651

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.61
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000156607

Normal statistic for number of bits   :    1.24
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:43.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 43  Permutation, t = 10             0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 115310613.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997324
  j =  2                              :             1335
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5358
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:57.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4465
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:57.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:05.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7177
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:05.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:55.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:59.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:13.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:40.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.60
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.08
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.37
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.44
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  271.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  472.20
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1475.50
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6888.75
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.29
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.93
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:04.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.48
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.24
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5085.84
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:58.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46146
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870146
  j =  1                              :        399907712
  j =  2                              :            46138
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908187
  j =  2                              :            45905
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:27.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:18.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:02.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  8.3e-3

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:39.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:38.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.19
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.78
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.66
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.23
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.22
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.98
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.14
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.05
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:39.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17510.18
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.89
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.55
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.87
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.97
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.64
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.32
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.10
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.43
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.77
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.12
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.84
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.90
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.22
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.03
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.57
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.94
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.40
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.60
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.51
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.66
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.00
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.29
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.18
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.51
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.06
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.19
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.04
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.78
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.12
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.34
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    1.53
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:23.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.84
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    2.62
p-value of test                       :  4.4e-3



-----------------------------------------------
CPU time used                    :  00:02:23.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
p-value of test                       :    0.9913

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.10
p-value of test                       :    0.02

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.99e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 6.68e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.94
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.61
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.93
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:04.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:04.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10248.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10177.75
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.082
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:41.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.58
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4795.14
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:51.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.09
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11887.65
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12052.32
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.32
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000102349

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.47
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000077098

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:42.44

 All tests were passed




Server wird beendet - Lösche Semaphor 116326421.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5527
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:56.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:58.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:04.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:03.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:54.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:59.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    2.20
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.55
p-value of test                       :  4.8e-3

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    2.10
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.37
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:12.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:40.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.03
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.03
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.74
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.05
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.11
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.33
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  192.97
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:44.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1401.31
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:02.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6943.04
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.17
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.17
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.98
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.68
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:31.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4825.48
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:58.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45822
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869822
  j =  1                              :        399908357
  j =  2                              :            45820
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46017
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870017
  j =  1                              :        399907971
  j =  2                              :            46007
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:27.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :  2.8e-3

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:19.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:55.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:35.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.08e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:33.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.43
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.61
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.25
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.12
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   47.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.92
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.11
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.46
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17738.18
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.25
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.26
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.38
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.45
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.37
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.19
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.11
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.43
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.53
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.03
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.87
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.79
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.84
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.04
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.13
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.08
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.47
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.03
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.48
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.88
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5131.39
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.09
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.45
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.92
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.61
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5126.99
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.40
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.25
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.40
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:24.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.86
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:21.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.07e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 6.24e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.65
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.55
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:03.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.52
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:05.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10159.85
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:42.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.73
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5073.44
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.82
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.09
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.37
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11654.28
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:29.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.84
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000068494

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   95.99
p-value of test                       :  3.8e-4    *****


-----------------------------------------------
Total number of bits:  8000107416

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.070
p-value of test                       :    0.53

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:34.46
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 102  Run of bits, r = 27             3.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 117309461.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5504
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:54.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:41.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:57.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:05.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:05.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:55.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:59.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    3.43
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    2.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:51.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:15.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9921

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:42.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.35
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.22
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.52
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.68
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.37
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.42
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.91
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:02.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7128.33
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.11
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:04.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  150.09
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:33.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.69
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:55.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45524
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869524
  j =  1                              :        399908956
  j =  2                              :            45516
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45827
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869827
  j =  1                              :        399908347
  j =  2                              :            45825
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:26.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:18.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:46.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:01.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.29e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 3.54e-4
p-value of test                       :  6.6e-3

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.71
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.30
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.56
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.79
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.95
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:41.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.85
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.80
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.15
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:39.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17491.72
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.24
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.25
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.04
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.10
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.97
p-value of test                       :  6.3e-3


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.66
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.11
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.40
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.31
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.55
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.31
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.78
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.78
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.92
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.76
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.22
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.81
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.45
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   47.75
p-value of test                       :    0.9924


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.14
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.51
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.79
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.11
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.28
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.66
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.05
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5098.30
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.10
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.51
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.51
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   0.070
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:22.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.33
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:21.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.93
p-value of test                       :    0.97

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.02e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.02e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.92
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.27
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.85
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:03.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.71
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:05.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10129.01
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9883.10
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:38.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:50.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.27
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11850.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11582.86
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.86
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000065443

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.35
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000076450

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   0.063
p-value of test                       :    0.47

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.048
p-value of test                       :    0.48

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:21.70

 All tests were passed




Server wird beendet - Lösche Semaphor 118292510.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:55.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:42.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:05.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:05.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:57.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:00.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:50.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.01
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.90
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:17.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:45.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.78
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.61
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.68
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.75
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.29
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1622.97
p-value of test                       :  4.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:02.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7303.90
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.02
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.58
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5060.05
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:04.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45584
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869584
  j =  1                              :        399908836
  j =  2                              :            45576
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45969
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869969
  j =  1                              :        399908064
  j =  2                              :            45965
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:28.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:17.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:45.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:59.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:54.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.96e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:31.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.95
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.86
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.89
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.22
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.89
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:39.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17376.72
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.39
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.45
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.25
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.84
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.18
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.31
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.03
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.74
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.25
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.22
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.86
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.71
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.47
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.17
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.24
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.65
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.19
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.82
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.62
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.09
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5217.39
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.45
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.44
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.28
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.57
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.77
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.66
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.33
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.00
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   0.025
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:21.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.49
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:21.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.41e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 6.07e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.39
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.57
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.16
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:05.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.07
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:04.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9747.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10234.07
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.079
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:37.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.77
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.86
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.82
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4281.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11675.13
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.61
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.93
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999971690

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.09
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000019309

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:12.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 36  Gap, r = 0                      4.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 119308318.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5350
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:58.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:45.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:00.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4171
p-value of test                       :    0.9942


-----------------------------------------------
CPU time used                    :  00:02:00.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:11.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:11.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:10.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:14.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     958
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:51.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:16.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.77
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:46.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.52
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.05
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.07
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:56.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1400.47
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:07.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7000.27
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:57.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.82
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.04
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:19.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.39
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:47.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.24
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:43.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5167.16
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:03.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46024
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870024
  j =  1                              :        399907956
  j =  2                              :            46016
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46233
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870233
  j =  1                              :        399907538
  j =  2                              :            46225
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.16e-3
p-value of test                       :    0.9905

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    4.20
p-value of test                       :  7.0e-3


-----------------------------------------------
CPU time used                    :  00:02:32.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:21.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:52.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:10.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:38.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.56e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:24.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:02.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:04.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.65
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.54
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.41
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.93
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:51.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.66
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.86
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.99
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17728.27
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.57
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.95
p-value of test                       :    0.9956


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.76
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.17
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.21
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   71.25
p-value of test                       :  4.2e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.42
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.89
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.32
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.49
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.41
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.24
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.60
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.83
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.52
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.18
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.30
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.27
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.82
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.37
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.61
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.29
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.16
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.46
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.59
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.68
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.89
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.85
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.22
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.16
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   0.034
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:23.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.38
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   0.025
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:22.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.91e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 7.96e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.44e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.29
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.14
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.84
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:04.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:04.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10153.27
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9910.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.30
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:04:25.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.37
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:55.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5019.06
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4265.20
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.71
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.12
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:35.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11736.96
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:37.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.98
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999983396

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.09
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000118006

Normal statistic for number of bits   :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   0.079
p-value of test                       :    0.47

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    2.60
p-value of test                       :  5.4e-3

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:21.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 H (L=50, r=25)      4.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 120258590.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:52.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:58.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:05.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:56.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:00.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.14
p-value of test                       :    0.9993    *****

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:51.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.32
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    3.10
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     556
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    2.09
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    4.03
p-value of test                       :  8.5e-3

-----------------------------------------------
CPU time used                    :  00:02:18.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:44.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.72
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.21
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.21
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.33
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.20
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.29
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  377.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:02.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6831.28
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.17
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.56
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.71
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.98
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4812.87
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9903


-----------------------------------------------
CPU time used                    :  00:02:59.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45619
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869619
  j =  1                              :        399908765
  j =  2                              :            45613
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46339
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870339
  j =  1                              :        399907323
  j =  2                              :            46337
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:28.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:18.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:54.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.70e-4
p-value of test                       :    0.9991    *****

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:33.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.57e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:35.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.75
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.51
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.61
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.90
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.06
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17678.11
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.91
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.41
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.57
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.00
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.78
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.67
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   57.72
p-value of test                       :  9.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   48.21
p-value of test                       :  3.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.31
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.43
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.88
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.01
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.10
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.73
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.03
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.23
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.28
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.66
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.71
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.90
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.28
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.67
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.73
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.61
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.39
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:33.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.62
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.05
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4856.46
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.94
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.72
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.66
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:19.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.15
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:16.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.65e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.29e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.58
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.04
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.45
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:57.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9981.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.40
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:21.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.48
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.98
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.39
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11952.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.17
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000157453

Normal statistic for number of bits   :    1.24
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.46
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999989297

Normal statistic for number of bits   :  -0.085
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:58:18.52
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP, t = 3           0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 121405470.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5469
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:41.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:36.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:34.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4201
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:54.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:00.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:00.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:53.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7521
p-value of test                       :  9.3e-3


-----------------------------------------------
CPU time used                    :  00:03:59.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.54
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:51.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:09.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9915

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:35.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.25
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.26
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.37
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.60
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.36
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.27
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:52.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1401.01
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6959.16
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:50.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:02.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.15
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.64
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:36.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4944.81
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:11.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45924
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869924
  j =  1                              :        399908154
  j =  2                              :            45920
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46147
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870147
  j =  1                              :        399907711
  j =  2                              :            46137
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:26.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:16.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:59.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:52.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.017
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.31
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.39
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.34
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.13
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.72
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.04
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.51
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.78
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17260.87
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.72
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.01
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.28
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.73
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.71
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.68
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.90
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.30
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.24
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.69
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.93
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.10
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.70
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.92
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.03
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.20
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.09
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.16
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.93
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.03
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.21
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4866.76
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.39
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.25
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:34.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.75
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.22
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.31
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.40
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.08
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:33.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   34.17
p-value of test                       :  6.3e-4    *****


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:12.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.05
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:11.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.88

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.81
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.19
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.32
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:10.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.37
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:09.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.57
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.41
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:45.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.04
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5027.52
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4226.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.39
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11542.52
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11987.18
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.79
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999934664

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.59
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000102499

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9975

Tests on the sum of all N observations
Standardized normal statistic         :   0.017
p-value of test                       :    0.49

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:14:24.34
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0               6.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 101711876.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5314
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:43.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4452
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:52.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:01.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:01.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:54.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:58.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    2.47
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:10.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:46.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.57
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.69
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.41
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.59
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.53
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:45.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1596.75
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:02:06.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7204.11
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.75
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.33
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:08.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.03
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.63
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:39.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4951.52
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:18.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45863
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869863
  j =  1                              :        399908280
  j =  2                              :            45851
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45648
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869648
  j =  1                              :        399908707
  j =  2                              :            45642
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:15.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9921

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:53.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 6.91e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.40e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.05
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.88
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.96
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.89
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.60
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.66
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:32.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.50
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.80
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17317.98
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.27
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.67
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.67
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.43
p-value of test                       :    0.9963


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.51
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.29
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.58
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.98
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.73
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.67
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.36
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.47
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.14
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.91
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.97
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.92
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.74
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.59
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.10
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.80
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.99
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.65
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.37
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.65
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4874.34
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.01
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.27
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.10
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:24.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.80
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:24.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.39e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.85e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.05
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.88
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:07.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:08.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10109.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9837.34
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:04:15.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4996.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5052.70
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:52.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.59
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4286.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11990.80
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.15
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:32.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.21
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000154141

Normal statistic for number of bits   :    1.22
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.00
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000088468

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:44.03

 All tests were passed




Server wird beendet - Lösche Semaphor 103350276.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5433
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:49.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:39.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4468
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:57.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7145
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:08.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:09.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:06.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:13.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.93
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:15.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.04
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:44.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.09
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.60
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.92
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.24
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.40
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.65
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.17
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:58.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1288.63
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:02:08.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7186.06
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:02.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.65
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:11.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.48
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   84.67
p-value of test                       :    0.9927


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4868.45
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:57.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45969
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869969
  j =  1                              :        399908068
  j =  2                              :            45957
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45858
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869858
  j =  1                              :        399908289
  j =  2                              :            45848
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    4.01
p-value of test                       :  8.7e-3


-----------------------------------------------
CPU time used                    :  00:02:29.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.78e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:55.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9991    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:12.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:57.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:38.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.61e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.77e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:51.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.32
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.33
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.16
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.92
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:53.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.48
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.22e-3
p-value of test                       :    0.9934

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.29
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17320.24
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.43
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.34
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.55
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.67
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.58
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.27
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.00
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.60
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.20
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.54
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.97
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.23
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.93
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.85
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.54
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.33
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.11
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.21
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.43
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.61
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.57
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.01
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.66
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.55
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.98
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.91
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.83
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.96
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.57
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.10
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.36
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   0.034
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:23.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.15
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:24.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.70e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 5.06e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.42
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.05
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.02
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:26.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.12
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:28.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9886.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.17
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.36
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:01:13.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:04:37.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5089.94
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:52.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5029.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3958.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.97
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11655.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11832.31
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.25
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000038461

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.21
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000094027

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   0.017
p-value of test                       :    0.49

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:56.89

 All tests were passed




Server wird beendet - Lösche Semaphor 104431620.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:48.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.99

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5494
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:50.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4450
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4196
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:06.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:57.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:02.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:11.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:40.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.62
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.69
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.58
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.22
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.41
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.95
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  272.14
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1342.11
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7298.59
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:42.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.16
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.15
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:07.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.15
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.96
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5217.61
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:53.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46040
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870040
  j =  1                              :        399907923
  j =  2                              :            46034
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45938
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869938
  j =  1                              :        399908130
  j =  2                              :            45926
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:27.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:17.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:58.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:56.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:34.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.89e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.37e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.087
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.76
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.35
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.72
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.10
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.14
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:45.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.40
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.52
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17472.10
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.13
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.74
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.02
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.19
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.50
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.41
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.75
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.99
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.30
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.87
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.75
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.22
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.36
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.90
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.08
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.13
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.58
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.39
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.64
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.86
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.09
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.21
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.88
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.85
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.81
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.42
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.22
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.58
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.58
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.91
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:23.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.31
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:23.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.97

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 3.00e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.64
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.55
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:07.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:07.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10147.84
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9663.29
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.44
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:42.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:47.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.68
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.63
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4004.28
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11764.34
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.05
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.99
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999983963

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.13
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000015061

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:04.21

 All tests were passed




Server wird beendet - Lösche Semaphor 105512964.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5374
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:50.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:06.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:07.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:59.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:03.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     854
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    2.10
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:12.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    3.06
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.46
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.11
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.62
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.46
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.00
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.28
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.93
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:51.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:03.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7072.12
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.65
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:07.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.23
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.05
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5082.38
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:57.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45962
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869962
  j =  1                              :        399908079
  j =  2                              :            45956
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45801
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869801
  j =  1                              :        399908400
  j =  2                              :            45797
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:29.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:16.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:44.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:57.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 8.74e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.95e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:22.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:51.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.53
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.87
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.02
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.74
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.68
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.76
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.06
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17140.05
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.39
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.64
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.78
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.09
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.96
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.76
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.64
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.95
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.03
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.75
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.72
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.88
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.14
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.12
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.33
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.44
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.42
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.68
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.88
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.49
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.90
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.43
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.03
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.74
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.41
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.01
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.58
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.53
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.13
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.39
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:23.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.95
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:24.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.06e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.41e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 6.42e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.98
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.17
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.15
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:05.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:05.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10193.94
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :  5.2e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    4.85
p-value of test                       :  3.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9647.41
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:04:09.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.84
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:51.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4735.12
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:51.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4194.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11715.83
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.87
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:29.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.74
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999825920

Normal statistic for number of bits   :   -1.38
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.40
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999788711

Normal statistic for number of bits   :   -1.67
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   0.040
p-value of test                       :    0.48

Sample variance                       :    0.23
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:36.93

 All tests were passed




Server wird beendet - Lösche Semaphor 106496004.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5373
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:55.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7158
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:05.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:07.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:59.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:01.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:13.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:43.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.60
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.36
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.12
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  194.54
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.63
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:51.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:04.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7068.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:52.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.43
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:12.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.26
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.01
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:37.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5027.34
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:52.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45943
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869943
  j =  1                              :        399908116
  j =  2                              :            45939
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46070
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870070
  j =  1                              :        399907864
  j =  2                              :            46062
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:29.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:19.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:47.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:58.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.61
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.05
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.07
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.37
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.12
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.52
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.37
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.78
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17469.93
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.92
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.83
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.69
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.94
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.15
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.25
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.98
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.20
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.27
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.07
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.09
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.28
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.70
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   43.15
p-value of test                       :    0.9984


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.03
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.79
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.69
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.71
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.67
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.01
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.01
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.43
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.81
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.58
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.54
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4882.17
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.33
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.18
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.30
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:21.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.94
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:19.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 9.42e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 3.65e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.49
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.45
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.76
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:04.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10022.91
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9924.36
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:04:13.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.25
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4974.62
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:54.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.56
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11801.71
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11466.19
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:01:31.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.16
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000080725

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.07
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000034009

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:39.98

 All tests were passed




Server wird beendet - Lösche Semaphor 107544580.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5457
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:53.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:40.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4439
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:57.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:58.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:05.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7537
p-value of test                       :  5.6e-3


-----------------------------------------------
CPU time used                    :  00:03:05.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:59.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:04.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.19
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:16.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:44.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.33
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.55
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.27
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.38
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:06.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7241.27
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:08.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.35
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5012.00
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:59.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45922
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869922
  j =  1                              :        399908161
  j =  2                              :            45912
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45874
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869874
  j =  1                              :        399908254
  j =  2                              :            45870
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:30.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:16.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:03.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:36.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 9.30e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:47.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:47.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.99
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.72
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.92
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.64
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.11
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:46.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    4.14
p-value of test                       :  7.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.55
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.02
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.79
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.37
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17357.69
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.22
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.76
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.87
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.25
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.98
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.73
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.87
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.49
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.95
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.63
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.09
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.40
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.32
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.58
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.99
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.50
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.47
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.59
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.25
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.12
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.03
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.85
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.18
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.06
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.22
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.82
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.65
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    1.53
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:25.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.76
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:25.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.74e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.71e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.01
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.79
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.87
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:06.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.99
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.47
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.02
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:04:10.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.45
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:52.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.46
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:52.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.62
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.93
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12014.27
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.58
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999866375

Normal statistic for number of bits   :   -1.06
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.07
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000029401

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:46.76

 All tests were passed




Server wird beendet - Lösche Semaphor 108560388.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:54.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7133
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:07.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:06.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:01.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:07.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    2.00
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    2.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    2.24
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:14.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    3.57
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:44.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.84
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.48
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.94
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.14
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.63
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.02
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.48
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7133.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:50.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.66
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:08.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.26
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.18
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:37.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5042.38
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:59.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45735
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869735
  j =  1                              :        399908534
  j =  2                              :            45727
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45841
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869841
  j =  1                              :        399908323
  j =  2                              :            45831
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:31.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:20.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 4.62e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:46.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.054
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.56
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.85
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.21
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.75
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.92
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.68
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.37
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17254.49
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.61
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.65
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.39
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.61
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   57.76
p-value of test                       :  9.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.26
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.30
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.55
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.00
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.41
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.43
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.06
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.42
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.89
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.96
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  437.88
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.34
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.65
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.70
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.61
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4835.46
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.82
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.97
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.30
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.83
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.98
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.54
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.35
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.05
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:23.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.52
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:25.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.38e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 6.39e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.42
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.51
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.62
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:03.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.67
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:04.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10285.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9711.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:04:02.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4770.45
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:51.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4738.94
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:51.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3870.03
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3954.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11773.43
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11732.24
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:29.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.83
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999921389

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.70
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000015745

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.87
p-value of test                       :    0.97

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:26.68

 All tests were passed




Server wird beendet - Lösche Semaphor 109510660.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:49.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5460
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:53.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:05.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:05.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:55.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:01.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    2.52
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     958
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.94
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.24
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:14.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:47.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.09
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.83
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.57
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.76
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.80
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.52
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:44.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.23
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6894.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.36
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:05.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.13
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  153.41
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5049.27
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:59.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45962
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869962
  j =  1                              :        399908083
  j =  2                              :            45948
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45687
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869687
  j =  1                              :        399908630
  j =  2                              :            45679
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:29.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:18.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  4.6e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:45.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:00.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.45e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.67e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -8.49e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:39.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.53
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.76
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.55
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.02
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.66
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.32e-3
p-value of test                       :    0.9955

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.59
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.90
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.39
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17532.35
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.70
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.63
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.21
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.08
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.26
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.05
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.51
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.69
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.95
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.49
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.94
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.75
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.72
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.26
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.31
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.96
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.69
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  188.23
p-value of test                       :  2.0e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  103.79
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.96
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.99
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.62
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.25
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.92
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.92
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  444.53
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.67
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.81
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.25
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.93
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -1.97
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.65
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    2.47
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.57e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.95e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.09
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.27
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.85
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:04.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.41
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:03.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.13
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10153.55
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.051
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:33.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:46.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.91
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:50.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.17
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.37
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11500.69
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.03
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999944189

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.75
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000090145

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :  -0.052
p-value of test                       :    0.52

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:47.59

 All tests were passed




Server wird beendet - Lösche Semaphor 110559236.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  3.4e-3


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:54.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4172
p-value of test                       :    0.9939


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:04.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:05.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:55.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:00.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    2.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    2.49
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:15.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.87
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:42.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.87
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.35
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.72
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.39
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.00
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.14
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:44.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.78
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7190.56
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:41.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.33
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.14
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:04.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.61
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.64
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:32.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4918.77
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:58.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46081
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870081
  j =  1                              :        399907843
  j =  2                              :            46071
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45936
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869936
  j =  1                              :        399908132
  j =  2                              :            45928
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:28.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:19.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:00.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:33.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 3.38e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.16e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:39.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.13
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.10
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.96
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.56
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:43.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.55
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.13
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.77
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17625.88
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.40
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.92
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.66
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.95
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.53
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.57
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.32
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.12
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.99
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.02
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.89
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.80
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  559.95
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.56
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.18
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.05
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  603.83
p-value of test                       :  9.6e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.63
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.14
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.78
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.95
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4837.33
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.54
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.20
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.89
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.53
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.03
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.06
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.63
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:24.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.56
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   0.039
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:23.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 9.78e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.51
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.07
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:04.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.44e-3
p-value of test                       :    0.9965

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  243.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:05.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9908.17
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10189.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.067
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:36.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.75
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:49.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5050.13
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:51.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4001.53
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11476.95
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12081.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.29
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000026350

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.57
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999996716

Normal statistic for number of bits   :  -0.026
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    2.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:02.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 J (L=1000, r=20)    9.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 111542276.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:55.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:07.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:08.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:02.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:04.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9938

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.60
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    2.16
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:16.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    2.08
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:43.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.03
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.89
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.84
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.44
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.35
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.66
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.94
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:06.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7115.01
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.59
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:07.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.40
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.67
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4904.07
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:00.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45845
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869845
  j =  1                              :        399908313
  j =  2                              :            45839
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45947
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869947
  j =  1                              :        399908114
  j =  2                              :            45931
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:27.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:04.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.94e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 2.85e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.32
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.11
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.27
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:50.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.24
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.00
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.28
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:39.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17348.10
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.95
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.54
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.84
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.37
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.53
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.54
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.96
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.37
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.70
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.67
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.18
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.66
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.16
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.63
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.01
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.29
p-value of test                       :    0.9931


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  424.66
p-value of test                       :    0.9937


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.21
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.20
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.50
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.72
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.73
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.16
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.01
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.77
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.61
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.51
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.62
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.53
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.88
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:24.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.43
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:23.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.77e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.49
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.57
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.50
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:03.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.79
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:03.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9982.47
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.086
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:04:06.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.26
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:52.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.87
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:52.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.90
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4022.70
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11616.12
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.14
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.47
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000024397

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.23
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999911708

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
p-value of test                       :    0.9941

Anderson-Darling statistic = A2       :    4.84
p-value of test                       :  3.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -3.13
p-value of test                       :    0.9991    *****

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:58.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 104  AutoCor, d=3, r=0               0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 112558084.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:53.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:41.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:56.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:57.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:05.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:05.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:56.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:01.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.44
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:14.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:39.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.68
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.26
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.46
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.94
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  272.77
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  388.79
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:43.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.74
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:01.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7227.75
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.73
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.41
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:02.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.54
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  150.94
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:34.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4872.72
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:05.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45873
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869873
  j =  1                              :        399908258
  j =  2                              :            45865
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45669
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869669
  j =  1                              :        399908668
  j =  2                              :            45657
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:29.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:18.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:34.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.51e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 3.50e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:35.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:34.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.68
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.18
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.74
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.48
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.62
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.38
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.91
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.86
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17195.32
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.32
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.11
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.76
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.57
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.62
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.41
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.24
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.67
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.79
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.84
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.06
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.16
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.44
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.04
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.78
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.80
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.48
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  319.33
p-value of test                       :    0.9930


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5203.60
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  322.12
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.36
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.92
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.29
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.00
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.78
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.04
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.98
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    1.28
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:25.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.63
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:23.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.29e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.45
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.89
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.69
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:02.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:03.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9982.78
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.15
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:38.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.42
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.61
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:50.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.78
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.58
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11714.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11609.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.73
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000060292

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.94
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000132442

Normal statistic for number of bits   :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:12.03

 All tests were passed




Server wird beendet - Lösche Semaphor 113573892.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5337
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:53.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:41.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:59.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:08.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7485
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:08.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:02.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:06.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    3.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:13.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.57
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.17
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.44
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:48.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.77
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:04.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6911.55
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:52.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:09.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.13
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.33
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:36.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5045.59
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:54.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45936
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869936
  j =  1                              :        399908133
  j =  2                              :            45926
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45947
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869947
  j =  1                              :        399908108
  j =  2                              :            45943
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:30.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:19.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.54e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.088
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:45.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.47
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.25
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.75
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.19
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.03
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9940

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.72
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.47
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.67
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17275.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.65
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.89
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.31
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.37
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.08
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.60
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.87
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.26
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.14
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.52
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.05
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.11
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.26
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.04
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.41
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.30
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.08
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.46
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.96
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.12
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.54
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5275.22
p-value of test                       :  3.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.40
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.68
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.60
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.25
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.57
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  441.42
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.82
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.48
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:21.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.04
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:20.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.93e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.96e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 9.62e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.83
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.90
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:02.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:04.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9723.41
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9919.33
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.17
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:04:13.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-3
p-value of test                       :    0.9990

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5176.36
p-value of test                       :  2.2e-3

-----------------------------------------------
CPU time used                    :  00:01:51.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:52.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4232.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11730.88
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11760.34
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.03
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000107242

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.94
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000066805

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:48.20

 All tests were passed




Server wird beendet - Lösche Semaphor 114556932.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:55.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:42.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:01.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:09.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:08.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9905

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.58
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:13.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.14
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.08
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.28
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.00
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.22
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.92
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.62
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.50
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:55.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1348.78
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:07.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6933.67
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:52.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.09
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.03
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:02.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.86
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.42
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5112.18
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:59.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46050
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870050
  j =  1                              :        399907905
  j =  2                              :            46040
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45938
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869938
  j =  1                              :        399908126
  j =  2                              :            45934
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:29.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:23.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:38.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.08e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.18e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:38.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.99
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.69
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.26
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.28
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:53.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17408.63
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.42
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.22
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.05
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.82
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.81
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.74
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.31
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.94
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.05
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.06
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.29
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.98
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.28
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.41
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.83
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.95
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.48
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.53
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.47
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.55
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.40
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.48
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.19
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.07
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.19
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5127.32
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.50
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.25
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.58
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:20.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.54
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :    2.02
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:21.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.83e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.38
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.89
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.54
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:06.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10015.08
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.77
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4780.05
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.86
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.06
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3908.76
p-value of test                       :    0.9900

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11847.47
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:29.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11699.77
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:29.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.82
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999802931

Normal statistic for number of bits   :   -1.56
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.18
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999993425

Normal statistic for number of bits   :  -0.052
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:58.95

 All tests were passed




Server wird beendet - Lösche Semaphor 115638276.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:49.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5267
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:52.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:40.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:05.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7460
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:55.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7503
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:00.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:13.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:40.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.75
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.68
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   93.13
p-value of test                       :  7.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.43
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.92
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.29
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:43.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1466.03
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7134.47
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:42.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.47
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.84e-3
p-value of test                       :    0.9938

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.50
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:02.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.76
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.39
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:33.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4943.21
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:59.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45875
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869875
  j =  1                              :        399908251
  j =  2                              :            45873
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46080
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870080
  j =  1                              :        399907846
  j =  2                              :            46068
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:28.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:18.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:40.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 9.68e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.01
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.91
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.85
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.96
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.06
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.99
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-3
p-value of test                       :    0.9979

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.23
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.77
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17672.30
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.24
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.98
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.84
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.22
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.32
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.08
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.47
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.75
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.18
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.73
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.20
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.73
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  562.22
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.16
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.83
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.41
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.59
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.16
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.11
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.12
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.62
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.28
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4843.86
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.04
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.02
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  454.17
p-value of test                       :  7.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.84
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.67
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.77
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.96
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:34.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.94
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:20.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.99
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:21.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 7.62e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 3.70e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.55
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.38
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:03.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.94
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:04.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10124.68
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10215.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:36.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4767.14
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:45.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.22
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:51.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.39
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.21
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12158.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11724.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.46
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000082234

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.93
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999747389

Normal statistic for number of bits   :   -2.00
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:58.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 31  CouponCollector, r = 10         7.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 116588548.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:53.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7121
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:42.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:59.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:08.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:09.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:01.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:02.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.43
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    3.09
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.94
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.07
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:13.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:42.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.63
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.44
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.91
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.15
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.32
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.76
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.63
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.29
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.42
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.36
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:03.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7071.88
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.82
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.05
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.91
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5017.14
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:01.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45614
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869614
  j =  1                              :        399908774
  j =  2                              :            45610
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46139
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870139
  j =  1                              :        399907724
  j =  2                              :            46135
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:30.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:17.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:03.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:37.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.90e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.75e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:45.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:42.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.25
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.17
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.98
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.91
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.40
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.08
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.37
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.07
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.43
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17356.66
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.84
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   60.99
p-value of test                       :  4.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.25
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.27
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.78
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.64
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.58
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.72
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.81
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.81
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.05
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.09
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.38
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.23
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.15
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.52
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.15
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.33
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.80
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.21
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.08
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.00
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.49
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.47
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.57
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.74
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4869.15
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.78
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.90
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.62
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -1.11
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:20.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.93
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:20.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 7.37e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.03
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.24
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.85
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:06.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.47
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:07.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10160.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9831.99
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:04:08.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.40
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.58
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:52.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4048.52
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.82
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11793.08
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11990.77
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.77
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  8000135757

Normal statistic for number of bits   :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.11
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000173533

Normal statistic for number of bits   :    1.37
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   0.085
p-value of test                       :    0.47

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:13.54

 All tests were passed




Server wird beendet - Lösche Semaphor 117571588.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5461
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:53.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:41.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:42.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:06.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:56.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:02.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:45.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.03
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:12.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:44.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.14
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.13
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.85
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.50
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.10
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.87
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.37
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7083.66
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.76
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:02.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.28
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.08
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:34.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5108.45
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:00.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45950
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869950
  j =  1                              :        399908102
  j =  2                              :            45946
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45600
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869600
  j =  1                              :        399908804
  j =  2                              :            45592
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:27.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:45.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:58.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:56.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:35.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.82e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.24
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.41
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.23
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.39
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.75
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.64
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.93
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.45
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16998.51
p-value of test                       :    0.9900



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.79
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.80
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.31
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.86
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.60
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.28
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.70
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.98
p-value of test                       :    0.9946


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.88
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.42
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.23
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.31
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.17
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.04
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.84
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.73
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.28
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.19
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.03
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.55
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.91
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.12
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.05
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.09
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.35
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.51
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4882.03
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.93
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  242.66
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.72
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:18.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.80
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:18.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.06e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.68
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.30
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.76
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.11
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10239.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9827.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.96
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:38.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.6e-3

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5058.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.23
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12126.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11663.21
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.40
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999998330

Normal statistic for number of bits   :  -0.013
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.93
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999967517

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.08

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:47.12

 All tests were passed




Server wird beendet - Lösche Semaphor 118652932.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:39.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1247
p-value of test                       :    0.9993    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334367
  j =  1                              :        599997506
  j =  2                              :             1247
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5404
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:54.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:43.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:01.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7123
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:10.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:10.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:04:07.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:08.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.86
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:51.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    2.29
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     533
p-value of test                       :    0.9971

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.17
p-value of test                       :    0.9960

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:13.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:39.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.33
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.78
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    5.88
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.06
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.77
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.05
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:53.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.68
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:03.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6954.68
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:56.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.93
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.50
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:15.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.08
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.56
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5073.83
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9925


-----------------------------------------------
CPU time used                    :  00:03:01.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45988
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869988
  j =  1                              :        399908026
  j =  2                              :            45984
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46110
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870110
  j =  1                              :        399907783
  j =  2                              :            46104
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.52
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:32.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:20.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:53.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:07.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:37.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.08e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 9.50e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 6.08e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:24.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.023
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.73
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.21
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:51.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.55
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.99
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17215.57
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.90
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.07
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.77
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.51
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.27
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.12
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.36
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.34
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.94
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.00
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.25
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.04
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.62
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.65
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.39
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.76
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.46
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.18
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.87
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.16
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.67
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.01
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.64
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.92
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.65
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.97
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.51
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    1.82
p-value of test                       :    0.9996    *****


-----------------------------------------------
Normal statistic for number of jumps  :  -0.069
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:23.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.98
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:20.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.83e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.09e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 7.86e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   21.77
p-value of test                       :  5.4e-3

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.44
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:02.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.1e-3

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  243.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10083.88
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:04:21.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.79
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:53.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.18
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:57.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.34
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.71
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11900.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:33.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12030.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:33.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.76
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000035386

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.13
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000068011

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   0.075
p-value of test                       :    0.47

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:40.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  5  CollisionOver, t = 3            0.9993 
 80  LinearComp, r = 0               0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 119635972.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5399
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:55.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4221
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7149
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:05.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:04.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:56.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:01.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:13.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:44.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.77
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.18
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.67
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.19
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1536.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7035.76
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:42.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.36
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.58
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:03.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.25
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.90
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:34.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.29
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:00.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45771
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869771
  j =  1                              :        399908458
  j =  2                              :            45771
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46009
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870009
  j =  1                              :        399907983
  j =  2                              :            46007
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:29.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:51.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:07.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.50e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:35.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.02e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:34.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.89
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.61
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.61
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.41
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.68
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.72
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.19
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17258.18
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.39
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.32
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.76
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.64
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.39
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.06
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.13
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.08
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.93
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.93
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.33
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.80
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.78
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.34
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.50
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.56
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.59
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.61
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.01
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.25
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.83
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5200.79
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.92
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.98
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.46
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.18
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.58
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.24
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.41
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.49
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:22.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.52
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:21.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    2.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.96e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.81
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.32
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.41
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:04.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.58
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:05.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9865.43
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10114.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.043
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:36.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4785.20
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:51.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.66
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.35
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.86
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.39
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000057187

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.62
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999864713

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   0.017
p-value of test                       :    0.49

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:34.19

 All tests were passed




Server wird beendet - Lösche Semaphor 120651780.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5371
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7152
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:43.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:59.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:07.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:06.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:58.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:02.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    2.42
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:15.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.65
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.13
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.68
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.99
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  182.63
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.70
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.66
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:04.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6913.45
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.52
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.63
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:10.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.00
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.11
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:37.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5066.55
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:01.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869892
  j =  1                              :        399908222
  j =  2                              :            45880
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45687
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869687
  j =  1                              :        399908627
  j =  2                              :            45685
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:29.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:16.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-3
p-value of test                       :    0.9975

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.62
p-value of test                       :  4.5e-3


-----------------------------------------------
CPU time used                    :  00:01:47.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:03.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 9.05e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 6.23e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:20.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:20.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:37.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.69
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.15
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:48.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.28
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.20
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:40.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.14
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.48
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17516.00
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.48
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.26
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.10
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.77
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.65
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.19
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.76
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.02
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.95
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.10
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.79
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.57
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.68
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.18
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.36
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.10
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.01
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.82
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  180.72
p-value of test                       :  6.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.61
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:40.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.77
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.86
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.51
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.49
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.89
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.23
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.49
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.21
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.43
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.62
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.01
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:11.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.10
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:11.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.67e-3
p-value of test                       :    0.9929

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.93
p-value of test                       :    0.03

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.02e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.27e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 9.28e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.55
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.13
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:15.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:53.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:53.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9936.12
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:50.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:19.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5098.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.66
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:42.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4258.06
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.77
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11823.45
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.02
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.83
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000108709

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.14
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999906257

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:59:05.18

 All tests were passed




Server wird beendet - Lösche Semaphor 121634820.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:41.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7115
p-value of test                       :    0.9914


-----------------------------------------------
CPU time used                    :  00:02:34.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:01.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:01.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:53.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:57.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.40
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    3.73
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:52.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:09.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:33.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.04
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.00
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.61
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.83
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.21
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.85
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.47
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:53.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:02.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7022.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:50.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.38
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.62
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:00.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.08
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.34
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4840.05
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:18.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46163
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870163
  j =  1                              :        399907678
  j =  2                              :            46155
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45868
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869868
  j =  1                              :        399908265
  j =  2                              :            45866
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:26.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:16.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:44.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:52.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:34.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.26e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.74e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.54e-6
p-value of test                       :    0.9983

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:35.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.63
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.35
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:44.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.02
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.32
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:31.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17277.12
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.15
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.80
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.68
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.23
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.38
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.65
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.92
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.24
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.40
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.95
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.79
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.62
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.50
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.82
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:47.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.38
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.77
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  561.83
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.94
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.53
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.84
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.79
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.56
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.84
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:34.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.62
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.90
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.04
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.94
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.90
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:33.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.49
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:12.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.75
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -1.29
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:11.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:11.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.48e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :  7.0e-3

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:47.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 2.03e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.53
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.92
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.80
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:11.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.85
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:09.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9974.29
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.13
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:54.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.93
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4743.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.26
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11921.77
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11957.15
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.71
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000018946

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.50
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999949115

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.63
p-value of test                       :    0.05

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.75
p-value of test                       :    0.04

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:15:02.32

 All tests were passed




Server wird beendet - Lösche Semaphor 101744645.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5490
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:42.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:36.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:34.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:54.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:54.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:00.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:01.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7172
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:52.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:58.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     267
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:11.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.67
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.79
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.17
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.09
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.98
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.71
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.75
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.60
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.07
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6835.23
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.98
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:02.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.11
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:35.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5090.24
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:59.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45656
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869656
  j =  1                              :        399908691
  j =  2                              :            45650
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46042
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870042
  j =  1                              :        399907920
  j =  2                              :            46034
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:28.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:18.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.19e-3
p-value of test                       :    0.9930

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:53.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.75
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:48.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.83
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.22
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.00
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.34
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.65
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.93
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17424.23
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.32
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.83
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.88
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.68
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.17
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.47
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.55
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.89
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.04
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.14
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:40.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.27
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.93
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.03
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.59
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.34
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:46.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.83
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.41
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.22
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   99.38
p-value of test                       :    0.9922


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.78
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.76
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.65
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5240.72
p-value of test                       :  8.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.82
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.33
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.68
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.13
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5310.82
p-value of test                       :  1.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.36
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  241.47
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.77
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   -1.65
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:15.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.61
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :   0.034
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:16.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 7.36e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:47.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.23e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.05
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.27
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.40
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:08.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:10.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10181.09
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10152.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.037
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:43.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5032.26
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.51
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4226.14
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.29
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11790.21
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.44
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.86
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999945374

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.10
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000058123

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:26.48

 All tests were passed




Server wird beendet - Lösche Semaphor 103415813.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5514
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:44.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:37.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:36.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:54.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:54.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:00.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:00.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:51.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:57.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    2.38
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     837
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    3.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.32
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:11.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:08.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:39.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.54
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.64
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.73
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.05
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  198.27
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.48
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.66
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6889.76
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:44.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-3
p-value of test                       :    0.9981

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   51.39
p-value of test                       :  8.9e-3

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:02.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.64
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.77
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:34.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4968.33
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:58.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45629
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869629
  j =  1                              :        399908745
  j =  2                              :            45623
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46165
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870165
  j =  1                              :        399907673
  j =  2                              :            46159
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:27.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:20.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:45.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:00.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.042
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:34.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:33.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.76
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.12
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.38
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.69
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9959

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.87
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.14
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17599.96
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.65
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.14
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.00
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.27
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.46
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.53
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.68
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.71
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.00
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.80
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.36
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.15
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.45
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.99
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.12
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.93
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.95
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.98
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.84
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.59
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.26
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.31
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  245.80
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  460.38
p-value of test                       :  4.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.17
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.20
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.58
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.54
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.76
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:16.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.26
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:16.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 5.61e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 6.56e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.29
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.62
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:08.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.59
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:07.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9815.69
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10019.77
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:53.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5027.99
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4747.06
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.69
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4016.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.89
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11626.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.05
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000002866

Normal statistic for number of bits   :   0.023
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.58
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000062632

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.84
p-value of test                       :    0.97

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.05
p-value of test                       :    0.02

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:39.29

 All tests were passed




Server wird beendet - Lösche Semaphor 104202245.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1259
p-value of test                       :    0.9979

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334379
  j =  1                              :        599997482
  j =  2                              :             1259
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:46.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:38.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7486
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:37.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7468
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:01.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:01.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:54.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:58.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:12.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.18
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:39.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.67
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.16
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.97
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.52
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.29
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:46.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1387.29
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:05.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7259.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:46.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.01
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.07
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:04.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.66
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.86
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5086.71
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:58.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45616
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869616
  j =  1                              :        399908771
  j =  2                              :            45610
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45873
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869873
  j =  1                              :        399908254
  j =  2                              :            45873
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:27.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:17.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:45.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:54.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.66e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.82e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:32.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:31.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.94
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.86
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.51
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:41.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.77
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.22
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.48
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17277.49
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.71
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.47
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.02
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.71
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.90
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.68
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.24
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.81
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.65
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.32
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.59
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.85
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.40
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.98
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.32
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.37
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.65
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.02
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.50
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.27
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.18
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.47
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.42
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  310.19
p-value of test                       :    0.9977


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.18
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4852.46
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.57
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.68
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.97
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    1.74
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:22.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.33
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:19.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 5.38e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.74e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.92
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.58
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:05.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.25
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10102.55
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.14
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.042
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:45.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4781.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4968.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.41
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12053.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12041.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:29.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.83
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999975881

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.93
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000145432

Normal statistic for number of bits   :    1.15
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   0.061
p-value of test                       :    0.48

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:25.77

 All tests were passed




Server wird beendet - Lösche Semaphor 104923141.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5327
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:49.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7124
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:02.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:01.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7500
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:54.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:00.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.40
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.17
p-value of test                       :    0.9958

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    3.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:11.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:40.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.62
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.67
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.00
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.14
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.08
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.13
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.05
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6867.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.44
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:02.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.85
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.46
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:35.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.58
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:00.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45296
p-value of test                       :    0.9968


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869296
  j =  1                              :        399909412
  j =  2                              :            45288
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45794
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869794
  j =  1                              :        399908414
  j =  2                              :            45790
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:28.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:19.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.38e-3
p-value of test                       :    0.9952

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 2.47e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 3.47e-4
p-value of test                       :  8.0e-3

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:35.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:34.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.66
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.49
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.98
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.35
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.93
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.77
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.50
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.95
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17531.64
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.67
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.44
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.94
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.28
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.96
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.49
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.94
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.75
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.20
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.73
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.46
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.63
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.13
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.61
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.34
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.83
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.03
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.19
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.10
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.43
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.75
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4788.30
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  322.14
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.15
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.25
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.48
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.03
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.04
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.01
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.75
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:20.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.79
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.25e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.41e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.79
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.26
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.01
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:07.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:07.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10145.99
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10089.45
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.41
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:52.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4991.38
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.97
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.96
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4241.64
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.56
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.04
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.01
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000095227

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.54
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000205225

Normal statistic for number of bits   :    1.62
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:41.15

 All tests were passed




Server wird beendet - Lösche Semaphor 105840645.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5349
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:52.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:39.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:02.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:02.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:52.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:57.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.70
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:14.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:36.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.21
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.02
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.41
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.25
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.23
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  492.39
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.54
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:02.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6767.05
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.06
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.16
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:04.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.19
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.24
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5075.03
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:54.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45342
p-value of test                       :    0.9940


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869342
  j =  1                              :        399909320
  j =  2                              :            45334
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45761
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869761
  j =  1                              :        399908480
  j =  2                              :            45757
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:26.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:19.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  4.0e-3

Kolmogorov-Smirnov- statistic = D-    : 5.57e-3
p-value of test                       :    0.9938

Anderson-Darling statistic = A2       :    4.45
p-value of test                       :  5.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9984


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:59.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.17e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.93e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.036
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.07
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.16
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.27
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.59
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.69
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:38.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.47
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  162.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17305.94
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.98
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.93
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.19
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.01
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.57
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.22
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.25
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.41
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.34
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.77
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.05
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.00
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.21
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.47
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.78
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.02
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.53
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.79
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.61
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4844.00
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.88
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.44
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.99
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.28
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4814.40
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.41
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.92
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.64
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:18.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.35
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    1.43
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.19e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.54
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.47
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:06.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.36
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.06
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10150.94
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:41.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:48.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.01
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4048.38
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.63
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11811.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11847.42
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.87
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000069496

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.22
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999972653

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :  9.8e-4    *****

Anderson-Darling statistic = A2       :    5.81
p-value of test                       :  1.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.03
p-value of test                       :  1.2e-3

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:48.67

 All tests were passed




Server wird beendet - Lösche Semaphor 106790917.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:55.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:03.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:03.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:55.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:58.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.38
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    2.03
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    2.23
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:14.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.07
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:46.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.10
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.49
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.90
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.13
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.96
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.32
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.29
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:45.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.80
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:02.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7196.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:45.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.44
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:03.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.77
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.60
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:34.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4896.51
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:16.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46018
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870018
  j =  1                              :        399907965
  j =  2                              :            46016
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46096
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870096
  j =  1                              :        399907811
  j =  2                              :            46090
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:27.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:18.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 4.14e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 2.52e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:33.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:32.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.63
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:48.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.00
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.53
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.70
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.43
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.01
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.48
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17304.80
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.07
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.42
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.30
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.55
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.07
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.78
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.82
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.65
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.43
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.87
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.19
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.74
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.18
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.46
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.63
p-value of test                       :    0.9940


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.19
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.19
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.54
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.73
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.09
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.19
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.50
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.47
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.49
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.19
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.84
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.57
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.59
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.44
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:20.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.16
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:19.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 2.05e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 5.06e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.05
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.88
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.45
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:05.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.17
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:07.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.87
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10130.05
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.38
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:03:39.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.30
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.45
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.14
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11879.88
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11502.63
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.02
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000057298

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.86
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000071830

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :  -0.079
p-value of test                       :    0.53

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:44.07

 All tests were passed




Server wird beendet - Lösche Semaphor 107773957.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5393
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:57.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:05.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:04.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:54.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:58.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.03
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    4.16
p-value of test                       :  7.3e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     266
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:14.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.89
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:37.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.13
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.94
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.70
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.22
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.90
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.30
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.29
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1378.31
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:02.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.14
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:01.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.35
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.67
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:33.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4981.50
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:00.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46166
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870166
  j =  1                              :        399907675
  j =  2                              :            46152
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45921
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869921
  j =  1                              :        399908162
  j =  2                              :            45913
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:26.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:57.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:33.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.69e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.48e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 9.81e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:35.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.09
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:48.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.01
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.13
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.39
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.67
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.09
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.69
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:12.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.38
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.52
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.09
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.70
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17450.27
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.00
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.94
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.94
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.12
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.66
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.86
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.09
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.63
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.10
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.35
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.94
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.93
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.54
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.53
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.84
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.28
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.80
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.12
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.68
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.04
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.31
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5149.73
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.16
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.19
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.60
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.70
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.19
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.40
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.93
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.32
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :    2.10
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:22.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.97
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   -1.46
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:21.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.98e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 9.74e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.89
p-value of test                       :  7.5e-3

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.55
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.23
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:06.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10073.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.31
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:41.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5053.78
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5000.62
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:49.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3994.87
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4239.76
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11883.57
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11995.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.07
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000112672

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.37
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000012631

Normal statistic for number of bits   :   0.100
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.44
p-value of test                       :    0.9927

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.80
p-value of test                       :    0.04

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.01
p-value of test                       :    0.98

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:52.17

 All tests were passed




Server wird beendet - Lösche Semaphor 108756997.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1270
p-value of test                       :    0.9948

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334390
  j =  1                              :        599997460
  j =  2                              :             1270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:57.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4201
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:42.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:58.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:04.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:54.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:59.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    3.42
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     642
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    2.95
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:11.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    3.64
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:42.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.63
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.58
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.02
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.55
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.06
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7001.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.30
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.37
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:03.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.43
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.40
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5275.06
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:11.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:03.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45946
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869946
  j =  1                              :        399908109
  j =  2                              :            45944
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908339
  j =  2                              :            45826
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:26.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:17.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:02.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:33.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 5.76e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.45e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:33.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.70
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.49
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:39.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.27
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.90
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.77
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.52
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17108.82
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:52.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.45
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.31
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.99
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.54
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.18
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.12
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.70
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.28
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.19
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.10
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.61
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  444.74
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.23
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.77
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.09
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.29
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.84
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.77
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.08
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.98
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5125.16
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.85
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.02
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  310.14
p-value of test                       :    0.9977


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5137.79
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.99
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.66
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.93
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -1.61
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:22.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.43
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:21.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.30e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.52
p-value of test                       :    0.9924

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.17
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :  3.3e-4    *****

Anderson-Darling statistic = A2       :    6.76
p-value of test                       :  4.7e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  270.91
p-value of test                       :  6.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:04.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:05.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10038.79
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9802.16
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.015
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:40.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4994.59
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.86
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4194.81
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.80
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11825.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.50
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.37
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000019669

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.55
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000061996

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 4.89e-3
p-value of test                       :    0.9949

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.93

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:49.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 88  PeriodsInStrings, r = 0         6.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 109740037.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1463
p-value of test                       :  4.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334583
  j =  1                              :        599997074
  j =  2                              :             1463
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:59.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:43.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:58.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:07.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:05.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7125
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:58.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:01.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.11
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.72
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.97
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.48
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:13.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:41.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.98
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.61
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.04
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.83
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.21
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  262.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.68
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.94
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:04.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6967.76
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.23
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:05.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.86
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.79
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4979.11
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:04.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46322
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870322
  j =  1                              :        399907357
  j =  2                              :            46320
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45968
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869968
  j =  1                              :        399908067
  j =  2                              :            45962
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:29.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:17.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:02.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.22e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 6.86e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:39.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:39.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.05
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.30
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.38
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.24
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.84
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:44.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.05
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.54
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17700.46
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.68
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.39
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.62
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.09
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.32
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.20
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.95
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.86
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.69
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.04
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.18
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.00
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.30
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.12
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  565.87
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.61
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.46
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.36
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.58
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4827.47
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.15
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.89
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.32
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.82
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4744.47
p-value of test                       :    0.9952


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.81
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.53
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.29
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:21.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.07
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -1.49
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:22.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.23

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.56e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 6.51e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.02
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.42
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.22
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9858.09
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10185.20
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:04:10.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.69
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4685.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:52.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4985.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.11
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.39
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11963.77
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:30.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.64
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.53
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000051370

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.85
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999971111

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.13

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:15.85

 All tests were passed




Server wird beendet - Lösche Semaphor 110723077.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:58.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:42.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7495
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:43.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:06.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:07.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:59.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:03.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:13.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.78
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.71
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.57
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.58
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.26
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.20
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:44.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:05.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7128.96
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.97
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.05
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:06.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.01
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  147.04
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:36.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5026.53
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:58.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908188
  j =  2                              :            45903
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45578
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869578
  j =  1                              :        399908849
  j =  2                              :            45568
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.83e-3
p-value of test                       :    0.9980

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:29.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:19.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:01.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.61e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:42.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.66
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.89
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.06
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.08
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.77
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:46.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.54
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.09
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.89
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17404.07
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.75
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.14
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.40
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.59
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.87
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.82
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.69
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.31
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.58
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.72
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.85
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.58
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.22
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.55
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.62
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.69
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.20
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.82
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.35
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.67
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.04
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.63
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.93
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.11
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.82
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.86
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.76
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.79
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.76
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    1.38
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:22.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.50
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:21.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.43e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.30e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.35
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.30
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.40
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:03.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.69
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:07.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10179.36
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9911.09
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:04:12.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.20
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:51.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.99
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:53.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.90
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11735.15
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:31.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11687.80
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:30.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.74
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999931868

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.04
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000034012

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:55.86

 All tests were passed




Server wird beendet - Lösche Semaphor 111837189.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5325
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:57.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4229
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4457
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:05.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:55.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:59.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9923

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.12
p-value of test                       :    0.9997    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:12.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.09
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    3.64
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:39.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.09
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.29
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.51
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.32
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.56
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.04
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7189.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:44.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9964

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:03.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.60
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.52
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4985.34
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:59.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45879
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869879
  j =  1                              :        399908246
  j =  2                              :            45871
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45917
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869917
  j =  1                              :        399908173
  j =  2                              :            45903
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:27.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:18.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:54.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:33.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.47e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:32.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.48
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:48.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.41
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.09
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.41
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.23
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.86
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.85
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:37.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.86
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17441.25
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.73
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.29
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.71
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.04
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.79
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.80
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.88
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.66
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.92
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.94
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.91
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.90
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.61
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.88
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.65
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.11
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.08
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.10
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.31
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.28
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  323.37
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.85
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.31
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.71
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.40
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.39
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.18
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.00
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.22
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.94
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:23.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.81
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:23.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.41e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 5.76e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.42e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.36
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.72
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.61
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:03.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10120.29
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10116.54
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.032
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:39.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:49.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.90
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3971.81
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11751.36
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11509.41
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:29.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.09
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999864155

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.47
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000182002

Normal statistic for number of bits   :    1.44
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:29.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP1, t = 9          0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 112820229.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5443
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:56.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4462
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:04.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:55.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.34
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.88
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.84
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.28
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.36
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    2.87
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     266
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:15.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.92
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:39.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.68
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.01
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.27
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.01
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.82
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.25
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.45
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.91
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7120.52
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:04.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.97
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.69
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:34.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5083.35
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:58.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45966
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869966
  j =  1                              :        399908069
  j =  2                              :            45964
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45937
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869937
  j =  1                              :        399908129
  j =  2                              :            45931
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:28.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:19.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:02.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.39e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 9.34e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:33.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.08
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.92
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.56
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:48.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.73
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.42
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:36.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.98
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9967

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.35
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17278.73
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.38
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.27
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.42
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.88
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.92
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.38
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.08
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.87
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.83
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.88
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.29
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.62
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.79
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.15
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.85
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  564.22
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.44
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.34
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.21
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.42
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.48
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.68
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.78
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.74
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.00
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.42
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.95
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.15
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.46
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:23.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.62
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -1.15
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:24.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 5.36e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.98e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 7.25e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.82
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.70
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.04
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:04.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.81
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:05.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.68
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10315.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10216.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:38.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.16
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.86
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3949.44
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.56
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11834.21
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11856.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:29.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.24
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000212092

Normal statistic for number of bits   :    1.68
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.81
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000071458

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.24
p-value of test                       :    0.99

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:33.27

 All tests were passed




Server wird beendet - Lösche Semaphor 113836037.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.33

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5368
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:58.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7482
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:04.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:56.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:00.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     551
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    2.41
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:12.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:42.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.37
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.48
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.08
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.84
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:52.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.77
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:06.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7135.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.77
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.35
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   89.68
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:03:01.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.13
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.91
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4992.83
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:04.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46138
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870138
  j =  1                              :        399907727
  j =  2                              :            46132
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45503
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869503
  j =  1                              :        399908998
  j =  2                              :            45495
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:28.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:19.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:01.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:32.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.49e-6
p-value of test                       :    0.9983

Kolmogorov-Smirnov- statistic = D-    : 3.42e-4
p-value of test                       :  9.4e-3

Anderson-Darling statistic = A2       :    5.22
p-value of test                       :  2.2e-3

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:35.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:35.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.31
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.02
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.71
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.03
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.71
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  161.68
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17587.65
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.21
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.17
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.79
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.73
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.63
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.54
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.05
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.72
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.44
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.43
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  589.72
p-value of test                       :  3.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.25
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.79
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.63
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.70
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.76
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.40
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.48
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.42
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.73
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.28
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.12
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.23
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.86
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.81
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.93
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  319.40
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.18
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.05
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :   -1.23
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:23.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.88
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    1.15
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:23.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.23
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.06
p-value of test                       :    0.98

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.10e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.39
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.37
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:04.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.66
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:05.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.69
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10077.89
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:43.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.41
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.80
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:49.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4223.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.96
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11963.18
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11652.33
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.82
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000113161

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.34
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000008857

Normal statistic for number of bits   :   0.070
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    2.51
p-value of test                       :  7.2e-3

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:23.61

 All tests were passed




Server wird beendet - Lösche Semaphor 114851845.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5516
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:58.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:05.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:06.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:55.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7165
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:00.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     939
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.96
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:12.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:42.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.60
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.36
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.06
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.97
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.88
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  381.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1497.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:03.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6915.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:59.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.71
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.66
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5118.82
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:03.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45883
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869883
  j =  1                              :        399908237
  j =  2                              :            45877
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46097
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870097
  j =  1                              :        399907808
  j =  2                              :            46093
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:26.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:20.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:01.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:55.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:33.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.37
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.47
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.94
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.64
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.02
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.84
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:37.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.72
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.43
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17673.78
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.78
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.50
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.25
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.93
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.12
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.31
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.09
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.46
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.88
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.45
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.19
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.64
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.44
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.24
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.18
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  103.35
p-value of test                       :    0.9970


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.87
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  568.17
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.52
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.41
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.47
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.44
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4789.92
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.42
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.76
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.67
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.44
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.12
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  243.19
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.60
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:21.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.53
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:21.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.77e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.19e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.99
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.82
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.02
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:03.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.92
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:05.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10071.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9987.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:39.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.99
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:47.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:50.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.90
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.55
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12034.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11996.23
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.46
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999973607

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.93
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000077398

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.92

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.11
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:42.31

 All tests were passed




Server wird beendet - Lösche Semaphor 115867653.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:58.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:05.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:56.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:01.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.09
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:14.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:41.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.11
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.07
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.12
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.35
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.73
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.35
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:44.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1474.01
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:01.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6945.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:43.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.86
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.54
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:02.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.03
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.06
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5112.64
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:04.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46000
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870000
  j =  1                              :        399908003
  j =  2                              :            45994
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45854
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869854
  j =  1                              :        399908296
  j =  2                              :            45846
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:26.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:18.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:54.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 8.13e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:31.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.20
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.86
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.40
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.97
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.59
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.10
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.37
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17436.29
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.84
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.59
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.77
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.79
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.86
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.33
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.14
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.55
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.09
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.39
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.14
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.89
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.32
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.07
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.92
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.83
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.04
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.42
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.51
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.97
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.24
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.79
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.71
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.46
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.82
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.09
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.07
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.52
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.68
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.08
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    1.97
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:21.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.09
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:22.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.40e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.90e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.74e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.84
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.85
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.48
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:04.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.32
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:06.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.9e-3

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10222.77
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : -2.43e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:41.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.02
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:47.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.63
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:50.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.68
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4257.70
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.14
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11925.57
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.63
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000175015

Normal statistic for number of bits   :    1.38
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.90
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999957770

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   0.044
p-value of test                       :    0.48

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:23.12

 All tests were passed




Server wird beendet - Lösche Semaphor 116883461.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:58.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7137
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:42.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:04.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:05.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:59.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:02.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    3.77
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     948
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9933

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    2.47
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:13.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:44.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.55
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.46
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.96
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.93
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.66
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.96
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:43.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1381.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:01.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7070.30
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.61
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.21
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:02.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.04
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.58
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:33.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4967.95
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:17.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46279
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870279
  j =  1                              :        399907445
  j =  2                              :            46273
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46061
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870061
  j =  1                              :        399907883
  j =  2                              :            46051
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:20.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:27.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:18.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:01.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:33.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.54e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:33.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.32
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.51
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.89
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.22
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.38
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.34
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.08
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.81
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.57
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17642.43
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.00
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.93
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.69
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.92
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.90
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.35
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.83
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.81
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.53
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.60
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.83
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.87
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.09
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.99
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.30
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.56
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.37
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.66
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.82
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.94
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.22
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.91
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.38
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.27
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.03
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.61
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.65
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.44
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.87
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:21.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.56
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:21.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.59
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.35
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.00
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:04.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.56
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:05.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9880.75
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:46.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.20
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.03
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3990.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4325.75
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11673.52
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11947.49
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.48
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000138631

Normal statistic for number of bits   :    1.10
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.59
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000056260

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:25.72

 All tests were passed




Server wird beendet - Lösche Semaphor 117899269.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9943


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5457
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:57.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:43.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:04.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:06.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:59.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:01.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    4.50
p-value of test                       :  5.0e-3

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    3.72
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     334
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    4.76
p-value of test                       :  3.8e-3

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:15.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:43.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.81
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.58
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.68
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.21
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.84
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.42
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1373.55
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6913.77
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:43.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.23
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.01
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:02.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.02
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.36
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4998.27
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:15.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45871
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869871
  j =  1                              :        399908263
  j =  2                              :            45861
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45666
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869666
  j =  1                              :        399908671
  j =  2                              :            45660
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:25.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :  2.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:17.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:45.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:59.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:54.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:34.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.74e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.84e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 3.31e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:31.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.022
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.84
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.35
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:48.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.75
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.02
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.85
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.17
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.98
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.92
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17155.64
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.45
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.84
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.16
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.52
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.32
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.45
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.28
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.76
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.88
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.52
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.39
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.27
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.69
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.69
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.31
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.93
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.76
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.47
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.01
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.78
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.55
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5115.54
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.44
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.35
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.07
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.12
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5161.07
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.16
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.36
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.26
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:23.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.99
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:23.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    1.74
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.24e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.40e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 7.75e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.07
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.28
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.12
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:02.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.75
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:04.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9913.40
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10050.83
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:38.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.13
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:47.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.70
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:48.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4248.21
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4010.53
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.04
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.10
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.23
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000101656

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.14
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000075913

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 7.55e-3
p-value of test                       :    0.9919

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:06.90

 All tests were passed




Server wird beendet - Lösche Semaphor 118915077.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:39.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1464
p-value of test                       :  3.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334584
  j =  1                              :        599997072
  j =  2                              :             1464
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:57.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4451
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:42.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:06.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:06.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:59.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:02.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.94
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    2.97
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    3.33
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:13.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:43.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.00
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.56
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.03
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.08
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.62
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.63
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.69
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.19
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.81
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.80
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:01.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7250.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:43.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.07
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:04.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.00
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.31
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5090.46
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:18.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45874
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869874
  j =  1                              :        399908256
  j =  2                              :            45866
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45979
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869979
  j =  1                              :        399908043
  j =  2                              :            45977
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:25.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:22.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:33.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.08e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.81e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.81
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.78
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.06
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.38
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.42
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.38
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.27
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.29
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:38.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.38
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.13
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17781.66
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.46
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.43
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.04
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.62
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.99
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.15
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.65
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.76
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.52
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.13
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.73
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.47
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.36
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.79
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.06
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.37
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.61
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.69
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4777.30
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.71
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.88
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.80
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.39
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.03
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.87
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.50
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.99
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:22.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.88
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:23.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 5.43e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.16e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.36
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.94
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.19
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:05.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.36
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:04.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9719.69
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9876.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.010
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.82
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:03:37.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.12
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.36
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:50.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.79
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11711.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11975.43
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.06
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999982919

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.96
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000047233

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.034
p-value of test                       :    0.51

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:56.22

 All tests were passed




Server wird beendet - Lösche Semaphor 119930885.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997167
  j =  2                              :             1415
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5356
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:56.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7471
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:42.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4471
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7137
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:05.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:05.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:57.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:02.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:14.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.76
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:41.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.41
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.16
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.64
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.03
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.97
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1407.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6920.84
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.64
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.49
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:04.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.92
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.06
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5025.95
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:18.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45712
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869712
  j =  1                              :        399908579
  j =  2                              :            45706
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46269
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870269
  j =  1                              :        399907467
  j =  2                              :            46259
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:26.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:23.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:52.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:02.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:33.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.88e-6
p-value of test                       :    0.9975

Kolmogorov-Smirnov- statistic = D-    : 3.37e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    6.01
p-value of test                       :  9.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.092
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.60
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.20
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.98
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.00
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:48.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.23
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.41
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.18
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.45
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.97
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.26
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17409.96
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.93
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.73
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.54
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.48
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.60
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.75
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.85
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.97
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.15
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.77
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.68
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.35
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.90
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.58
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.48
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.57
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.38
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.43
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  306.04
p-value of test                       :    0.9987


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  450.17
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.35
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.55
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.11
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.49
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.21
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.02
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.11
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.50
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.80
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:21.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.26
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.69e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.80e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 9.91e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.96
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.11
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.54
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:05.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:04.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.69
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:35.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4795.66
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9984

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.34
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.69
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11781.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11867.87
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.71
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999967967

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.09
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000008296

Normal statistic for number of bits   :   0.066
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.97
p-value of test                       :    0.98

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:25.44
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 54  SampleMean, r = 10              9.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 120946693.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:41.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:36.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:34.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:01.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:01.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:51.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:57.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:52.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.03
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    3.32
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     658
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:10.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.93
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:35.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.66
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.40
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.23
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.18
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.41
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.68
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.49
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.59
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.40
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7029.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.13
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.06
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.51
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.17
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45950
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869950
  j =  1                              :        399908105
  j =  2                              :            45940
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46106
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870106
  j =  1                              :        399907791
  j =  2                              :            46100
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:28.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:15.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:52.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:33.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.53e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:24.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:33.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.14
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.07
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.79
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.81
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.74
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:33.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:31.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17390.74
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.85
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.98
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.85
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.97
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.09
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.92
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.50
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.60
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.84
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.18
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.89
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.81
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.40
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.22
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.55
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.95
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.56
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.33
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.09
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:48.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.00
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.49
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.56
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.01
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.86
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.57
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.48
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.85
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.42
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.13
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:17.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.28
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    1.48
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:12.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 3.78e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.18
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.99
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.63
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:09.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.04
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:10.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10274.47
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9912.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:42.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.07
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4745.12
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.93
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.73
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.90
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.85
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.80
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000231685

Normal statistic for number of bits   :    1.83
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.12
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999893510

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.59
p-value of test                       :  4.8e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.75
p-value of test                       :    0.9970

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:14:29.55

 All tests were passed




Server wird beendet - Lösche Semaphor 101777414.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:39.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:41.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:35.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:53.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:53.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:00.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:01.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:51.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:57.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     639
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9934

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    2.04
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:13.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    2.40
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.59
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.41
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.35
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.43
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.03
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.21
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.79
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:02.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7001.99
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:45.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.35
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:01.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.81
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.62
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:35.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5175.11
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:03.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45582
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869582
  j =  1                              :        399908839
  j =  2                              :            45576
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45677
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869677
  j =  1                              :        399908652
  j =  2                              :            45665
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:30.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:21.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:59.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:52.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.74e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:32.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:35.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.16
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.59
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.77
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.42
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.94
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.67
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.60
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.31
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.87
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:29.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.80
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17577.18
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.86
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.54
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.58
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.83
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.44
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.15
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.14
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.51
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.47
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.43
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.43
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   94.52
p-value of test                       :    0.9973


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.14
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.34
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.60
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.56
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.03
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.61
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.93
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.09
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.44
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.04
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.59
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.67
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.22
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.66
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.24
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.52
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:24.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.42
p-value of test                       :  6.7e-3


-----------------------------------------------
Normal statistic for number of jumps  :  -0.024
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:14.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 6.37e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 9.95e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.61
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.16
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.75
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:06.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:09.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9845.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10022.04
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.024
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:49.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4752.25
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:48.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:49.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.57
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.01
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11614.89
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12006.74
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.90
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000042310

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.35
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999933341

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:32.32

 All tests were passed




Server wird beendet - Lösche Semaphor 102825990.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:50.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997285
  j =  2                              :             1356
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1475
p-value of test                       :  1.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334595
  j =  1                              :        599997050
  j =  2                              :             1475
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5302
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:42.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:34.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:54.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:53.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:00.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:00.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:51.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:57.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    2.91
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.16
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.13
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:09.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:37.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.12
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.50
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.81
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.47
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.67
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:45.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1488.24
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7042.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:51.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.10
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:02.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.68
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:46.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.87
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:34.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4952.42
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:01.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45870
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869870
  j =  1                              :        399908266
  j =  2                              :            45858
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45938
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869938
  j =  1                              :        399908129
  j =  2                              :            45928
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:29.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :  2.6e-3

Anderson-Darling statistic = A2       :    3.98
p-value of test                       :  9.0e-3


-----------------------------------------------
CPU time used                    :  00:02:19.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:45.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:02.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.59e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:33.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.51
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.86
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.08
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.43
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:29.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.08
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17458.61
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.61
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.12
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.14
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.33
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.08
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.66
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.53
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.23
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.70
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.54
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.26
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.79
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.71
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.08
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.29
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.87
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.72
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.20
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.56
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.91
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.09
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.12
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.56
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.85
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.66
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.39
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.65
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:24.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.33
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:16.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.99e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.65e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.79
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.95
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.96
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:06.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.90
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:09.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.1e-3

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10259.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9872.88
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.17
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:47.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.77
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    4.75
p-value of test                       :  4.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4619.51
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4305.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3997.70
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12109.47
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.75
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:29.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.52
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000056425

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.32
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000076150

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 2.89e-3
p-value of test                       :    0.9970

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -2.16
p-value of test                       :    0.98

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:19.84

 All tests were passed




Server wird beendet - Lösche Semaphor 103841798.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:45.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4217
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:37.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:37.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:02.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:01.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:51.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7144
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:57.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    2.34
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9967

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:09.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     123
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:42.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.10
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.53
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.99
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.40
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.70
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.47
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.83
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:02.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7134.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.36
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.42
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.65
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4901.46
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:01.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45665
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869665
  j =  1                              :        399908674
  j =  2                              :            45657
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45861
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869861
  j =  1                              :        399908282
  j =  2                              :            45853
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:29.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:02.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:54.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:34.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 8.55e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:34.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.32
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.92
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.06
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.47
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.96
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.61
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:41.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.44
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.28
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.64
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17666.20
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.60
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.98
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.51
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.24
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.91
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.82
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.01
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.41
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.77
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.19
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.50
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.89
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.70
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.61
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.20
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.29
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.57
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.41
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.50
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.88
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.67
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.34
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.36
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.53
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.90
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5115.80
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.05
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.75
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.94
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:24.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.70
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:21.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.51e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 2.09e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.89
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.40
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9985

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.19
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:08.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.27
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:06.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.60
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10177.77
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.066
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:43.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.85
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4699.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:49.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.92
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3957.19
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11527.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11842.36
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.91
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999998165

Normal statistic for number of bits   :  -0.015
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.36
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999957950

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   0.028
p-value of test                       :    0.49

Sample variance                       :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:06.77

 All tests were passed




Server wird beendet - Lösche Semaphor 104792070.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5598
p-value of test                       :  8.5e-3


-----------------------------------------------
CPU time used                    :  00:03:49.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:03.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:00.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:52.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:57.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.88
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     846
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9938


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:11.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.65
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.03
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.41
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.52
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.98
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  280.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  364.98
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:01:45.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1315.64
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7234.73
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:44.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.47
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.95
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.87
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5123.07
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:59.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45752
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869752
  j =  1                              :        399908497
  j =  2                              :            45750
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45814
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869814
  j =  1                              :        399908377
  j =  2                              :            45804
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  8.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9915


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:28.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:17.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:01.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:55.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:33.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.05e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.27
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.61
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.48
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.83
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.74
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.66
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:41.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.30
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.83
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.04
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.90
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17598.41
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.89
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.31
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.52
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.76
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.84
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.42
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.58
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.77
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.12
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.65
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.27
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.29
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.35
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.55
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.22
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.24
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.44
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.94
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.21
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.40
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.58
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.47
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.50
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.23
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.92
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.30
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.16
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.19
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    1.26
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:21.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.92
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:21.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.46
p-value of test                       :    0.9931

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.05e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 9.02e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.56e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.89
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.35
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
p-value of test                       :    0.9910

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  254.96
p-value of test                       :  5.2e-3

-----------------------------------------------
CPU time used                    :  00:02:08.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.15
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:06.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10015.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10302.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.29
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:42.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4727.47
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.32
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4228.48
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11713.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12247.62
p-value of test                       :  3.3e-3

-----------------------------------------------
CPU time used                    :  00:01:29.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.47
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000024814

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.57
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999968018

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.69
p-value of test                       :    0.05

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.086
p-value of test                       :    0.53

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:06.96

 All tests were passed




Server wird beendet - Lösche Semaphor 105775110.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5336
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:53.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:03.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:51.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:56.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    3.33
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     643
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.76
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:11.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:36.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.38
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.71
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.17
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.68
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.12
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  380.46
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.31
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7003.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:44.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.61
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.70
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.24
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.42
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5268.26
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:58.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45864
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869864
  j =  1                              :        399908273
  j =  2                              :            45862
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46030
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870030
  j =  1                              :        399907942
  j =  2                              :            46026
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:29.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:18.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:46.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
p-value of test                       :    0.9928

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:34.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 6.64e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 2.94e-6
p-value of test                       :    0.9997    *****

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:31.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:31.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.37
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.44
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.77
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.76
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.94
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:38.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.69
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17540.15
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.81
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.21
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.42
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.91
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.37
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.37
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.48
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.31
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.85
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.14
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.54
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.39
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.94
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.05
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.23
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.30
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.03
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.32
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.25
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.89
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.21
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.46
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5187.85
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.51
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.89
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:34.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.24
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.00
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5167.69
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  448.59
p-value of test                       :  7.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.84
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:34.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.64
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:22.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.59
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -2.85
p-value of test                       :    0.9978



-----------------------------------------------
CPU time used                    :  00:02:23.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.43
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.61
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.09
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:05.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10082.96
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10063.55
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.066
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:42.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5028.29
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.47
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3941.53
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11598.57
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11948.44
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.90
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999918137

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.97
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999942344

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:18.62

 All tests were passed




Server wird beendet - Lösche Semaphor 106659846.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:58.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:43.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:59.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:08.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:06.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:57.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:59.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.20
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:11.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:38.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.04
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.65
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.65
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.39
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.71
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.88
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.22
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1565.13
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7044.54
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.64
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.91
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:07.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.52
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.28
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4990.26
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:58.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45767
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869767
  j =  1                              :        399908473
  j =  2                              :            45753
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45633
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869633
  j =  1                              :        399908734
  j =  2                              :            45633
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:30.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:19.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:06.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:36.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 9.92e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.96e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:36.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.79
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.30
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.47
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.28
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.29
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.74
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.90
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17305.07
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.48
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.25
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.40
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.71
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.26
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.66
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.40
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.30
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.08
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.18
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.67
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.19
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.37
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.67
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.28
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.20
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.34
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.51
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.64
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4915.09
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.11
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.79
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.13
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.66
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4852.36
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.11
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.18
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:34.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.10
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:20.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.36
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -1.20
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:23.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.16e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.55
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.15
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.89
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:08.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.11
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:05.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10063.98
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:04:13.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.04
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:53.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.12
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:53.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.19
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4179.01
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11921.75
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11942.84
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.14
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999968933

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.22
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999973646

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:14.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:18.54

 All tests were passed




Server wird beendet - Lösche Semaphor 107675654.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5518
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:56.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:04.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:04.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:53.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:59.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9937

-----------------------------------------------
CPU time used                    :  00:01:51.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.70
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    2.53
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:14.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    2.42
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:38.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.49
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.03
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.89
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.02
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.74
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.66
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:03.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6951.33
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.10
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.11
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.01
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5019.70
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:59.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45787
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869787
  j =  1                              :        399908432
  j =  2                              :            45775
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45774
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869774
  j =  1                              :        399908456
  j =  2                              :            45766
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:28.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:18.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:46.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:01.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:54.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    3.10
p-value of test                       :  9.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:32.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.64
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.41
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.01
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.80
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.37
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.26
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.58
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.84
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17105.89
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.46
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.27
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.84
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.65
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.95
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.49
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.82
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.12
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.75
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.63
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.21
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.11
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.95
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.18
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.20
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.11
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.63
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.10
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.03
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.64
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.08
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.87
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.15
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.35
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.03
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.94
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.40
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.36
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.93
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.03
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.40
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -1.43
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:22.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.28
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :  -0.051
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:25.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 7.15e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.34e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.57
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.19
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.60
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:05.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.29
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:04.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.08
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9885.90
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:44.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.91
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.12
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.64
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11646.45
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.46
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000002230

Normal statistic for number of bits   :   0.018
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.63
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000091663

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.3e-3

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.95
p-value of test                       :    0.03

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:36.55
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 58  AppearanceSpacings, r = 27      9.7e-4
 ----------------------------------------------
 All other tests were passed




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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5347
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:56.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:42.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:04.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:53.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:59.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.24
p-value of test                       :  6.8e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    3.84
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     649
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    3.26
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:13.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.47
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    2.59
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:41.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.97
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.14
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   89.21
p-value of test                       :  1.8e-3

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.08
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.63
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.23
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7192.90
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.47
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.73e-3
p-value of test                       :    0.9906

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:06.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  147.64
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5039.62
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:59.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46027
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870027
  j =  1                              :        399907949
  j =  2                              :            46021
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45661
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869661
  j =  1                              :        399908681
  j =  2                              :            45655
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:27.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:19.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:00.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:32.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.51e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.81e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 7.57e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   39.51
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.69
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.83
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:48.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.16
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.73
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:37.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.73
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.64
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.98
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17302.08
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.48
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.27
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.77
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.96
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.32
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.71
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.11
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.16
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.44
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.45
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.37
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.48
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.99
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.57
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.16
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.00
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.73
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.96
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.66
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.16
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.59
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.88
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.52
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.22
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5150.26
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.89
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.14
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.89
p-value of test                       :    0.9963


-----------------------------------------------
Normal statistic for number of jumps  :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:21.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.21
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:23.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.08
p-value of test                       :    0.02

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.87e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.17e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.59
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.09
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.32
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:07.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.08
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9766.58
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10130.32
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:38.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5058.39
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.62
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:49.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.57
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.87
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11716.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11622.75
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.46
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000026695

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.67
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999801425

Normal statistic for number of bits   :   -1.57
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:48.45

 All tests were passed




Server wird beendet - Lösche Semaphor 109838342.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1191
p-value of test                       : 1 -  8.9e-7    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334311
  j =  1                              :        599997618
  j =  2                              :             1191
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5346
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:56.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:03.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:54.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7498
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:59.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:13.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.33
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.13
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.44
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.16
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.94
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.77
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.11
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.38
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:01.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7344.25
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.89
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:02.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.19
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.35
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:35.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5076.06
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:57.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45690
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869690
  j =  1                              :        399908625
  j =  2                              :            45680
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45858
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869858
  j =  1                              :        399908286
  j =  2                              :            45854
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:28.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:19.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:55.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.82e-3
p-value of test                       :    0.9935

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 6.66e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:35.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.79
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.00
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.93
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.70
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.77
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.37
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.03
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.29
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.24
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.093
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.36
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17605.14
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.99
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.87
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.73
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.02
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.51
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.02
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.52
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.53
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.76
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.61
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.25
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.47
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.56
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.10
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.88
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.62
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.55
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.88
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.18
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.90
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.55
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.52
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.82
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.38
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.90
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.25
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.59
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.08
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.06
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   0.061
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:21.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.75
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:22.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    2.38
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.10e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 6.41e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.75e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.32
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.82
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:04.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.96
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:04.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 2.10e-3
p-value of test                       :    0.9979

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9724.52
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10078.38
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:42.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.37
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:49.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.44
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.19
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11960.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.20
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.03
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999900233

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.77
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000046657

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.63
p-value of test                       :    0.05

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:41.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21          1 -  8.9e-7
 84  Fourier3, r = 0                 0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 110821382.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  4.0e-3


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:59.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:42.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:43.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:06.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:06.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:59.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:04.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:13.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.04
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.73
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.70
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.24
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.75
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:45.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.52
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:05.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7243.21
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   84.89
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.06
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.05
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.08
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:58.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45401
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869401
  j =  1                              :        399909200
  j =  2                              :            45397
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46018
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870018
  j =  1                              :        399907966
  j =  2                              :            46014
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:29.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:18.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:45.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:02.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:36.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.01e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.043
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.075
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.01
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.02
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.48
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.30
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.15
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.73
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.31
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17454.29
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.51
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.91
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.83
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.83
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.19
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.41
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.67
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.19
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.67
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.16
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.92
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.86
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.22
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  566.07
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.82
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.36
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.84
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.20
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5143.19
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.60
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.81
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  322.15
p-value of test                       :    0.9904


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.36
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.89
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.32
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.77
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.03
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:21.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.89
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.95
p-value of test                       :    0.03

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.00e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.21
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.42
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:03.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.48
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:06.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9807.82
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.78
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:04:16.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.40
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5002.97
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:53.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.75
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.62
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.76
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:31.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.20
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.68
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999957761

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.83
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999997943

Normal statistic for number of bits   :  -0.016
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.062
p-value of test                       :    0.52

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:04.40

 All tests were passed




Server wird beendet - Lösche Semaphor 111804422.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1487
p-value of test                       :  5.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334607
  j =  1                              :        599997026
  j =  2                              :             1487
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:57.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:39.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4195
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:05.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:05.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:55.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:58.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     845
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:13.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:43.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.32
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.10
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.50
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.79
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  186.98
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.11
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:45.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1320.71
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7050.93
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.43
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:05.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.19
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5033.39
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:11.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:00.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45990
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869990
  j =  1                              :        399908028
  j =  2                              :            45974
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45576
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869576
  j =  1                              :        399908851
  j =  2                              :            45570
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:27.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:17.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:53.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 5.62e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.57
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.042
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:33.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.21
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.46
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.87
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.10
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.49
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.96
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:37.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.06e-3
p-value of test                       :    0.9958

Anderson-Darling statistic = A2       :    3.76
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   20.19
p-value of test                       :    0.9962

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17309.79
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.63
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.27
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.79
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.00
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.42
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.37
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.72
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.91
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.65
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.29
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.57
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.33
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.22
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.89
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.30
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.35
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.58
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.80
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.60
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.11
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.13
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.78
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.94
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.22
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.17
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.22
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.23
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.90
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.60
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.68
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:22.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.87
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :  -0.033
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:23.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.84e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.90e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 9.69e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.88
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.16
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.82
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:06.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  248.01
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:04.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10332.97
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10052.22
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:42.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.78
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.1e-3

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5051.11
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.69
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11938.05
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.34
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.56
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000088084

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.28
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999995663

Normal statistic for number of bits   :  -0.034
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:48.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           5.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 112852998.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1253
p-value of test                       :    0.9988

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334373
  j =  1                              :        599997494
  j =  2                              :             1253
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5532
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:57.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4186
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:05.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:05.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:55.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:59.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.22
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:15.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:42.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.59
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.64
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.30
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.45
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.06
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1387.87
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6903.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.69
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.12
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:02.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.44
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.30
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5000.57
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:59.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45547
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869547
  j =  1                              :        399908912
  j =  2                              :            45535
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45564
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869564
  j =  1                              :        399908874
  j =  2                              :            45560
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:28.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
p-value of test                       :    0.9905

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:33.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.34e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.90e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.14e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:47.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.26
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.12
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.32
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.49
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:39.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.89
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.83
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17406.96
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.02
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.92
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.95
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.71
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.77
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.64
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.01
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.97
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.39
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.14
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.84
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.18
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.00
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.23
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.02
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.81
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.38
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  444.17
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.45
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.13
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.79
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.96
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.81
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.07
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.26
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.89
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.30
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5139.92
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.97
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.30
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.97
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    1.42
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.65
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :  -0.033
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:24.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.01e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 9.41e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.27e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 4.71e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.00
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.13
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.01
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:05.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.72
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.00
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10094.44
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:38.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5074.52
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4774.92
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:49.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.81
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.41
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11539.29
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.85
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999871904

Normal statistic for number of bits   :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.36
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999872549

Normal statistic for number of bits   :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :  -0.074
p-value of test                       :    0.53

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:34.95

 All tests were passed




Server wird beendet - Lösche Semaphor 113868806.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  1.3e-3


-----------------------------------------------
CPU time used                    :  00:00:48.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:54.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:41.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:06.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:56.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7469
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:00.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     957
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.07
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:18.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.82
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:43.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.69
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.97
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   43.60
p-value of test                       :  6.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.00
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.33
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.22
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.21
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.02
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.85
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7108.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:43.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.88
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.68
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:02.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.78
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.19
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5152.96
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9973


-----------------------------------------------
CPU time used                    :  00:02:57.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46110
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870110
  j =  1                              :        399907788
  j =  2                              :            46094
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45995
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869995
  j =  1                              :        399908012
  j =  2                              :            45991
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:29.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:19.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:45.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:00.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:54.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.84e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 2.87e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.72e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.42
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:01:33.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.46
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.49
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.34
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:47.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.99
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.2e-3

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    6.64
p-value of test                       :  5.3e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.14
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.22
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.36
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17478.09
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.31
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.87
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.30
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.12
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.45
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.09
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.88
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.47
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.78
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.84
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.00
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.28
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.09
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.89
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.43
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.62
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.93
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.59
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.53
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.73
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.93
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.15
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.62
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.24
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.40
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.62
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.17
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.05
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.63
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.00
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :    2.50
p-value of test                       :  6.2e-3



-----------------------------------------------
CPU time used                    :  00:02:23.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.72
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:24.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.17

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.54e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.71e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.79
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.63
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.23
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:07.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10071.02
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10115.65
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:37.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.46
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.82
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.55
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11926.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.42
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999877610

Normal statistic for number of bits   :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.90
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000062839

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   0.091
p-value of test                       :    0.46

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:57.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 28  SimpPoker, r = 0                6.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 114884614.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1250
p-value of test                       :    0.9991    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334370
  j =  1                              :        599997500
  j =  2                              :             1250
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:57.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:42.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:57.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:09.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:09.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:01.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7488
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:00.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.24
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.19
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:14.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:44.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.45
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.30
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.61
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.03
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  362.81
p-value of test                       :    0.9945

-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.76
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6956.55
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.61
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:05.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.95
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.38
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:35.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4994.08
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:58.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45750
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869750
  j =  1                              :        399908505
  j =  2                              :            45740
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46007
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870007
  j =  1                              :        399907988
  j =  2                              :            46003
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:29.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:17.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:44.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:36.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 9.43e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.097
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:37.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:38.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.51
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.35
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.63
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  165.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17380.81
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.80
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.54
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.32
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.44
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.22
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.25
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.50
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.29
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.04
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.18
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.17
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.65
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.78
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.56
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.67
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.16
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.61
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.15
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.14
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  322.25
p-value of test                       :    0.9903


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.52
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4879.41
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.21
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.67
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.45
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.87
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.43
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.24
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.50
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.05
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:20.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.97
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.96

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 5.59e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.91e-4
p-value of test                       :    0.9929

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.36
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.53
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.82
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:07.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9851.55
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10174.55
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : 3.72e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:04:12.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.00
p-value of test                       :  9.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4640.98
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:01:51.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4701.51
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:53.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.38
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.94
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11646.81
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:30.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11945.93
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.01
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000086686

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.85
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999901334

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 2.25e-3
p-value of test                       :    0.9977

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.91

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:05.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  8  CollisionOver, t = 7            0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 115900422.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5405
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:56.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:09.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:00.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:05.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.64
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.94
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    2.90
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:13.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:45.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.20
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.64
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.62
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.47
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.63
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  473.25
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.61
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:05.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6937.89
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.40
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.58
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:06.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.01
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.03
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5004.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:59.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908337
  j =  2                              :            45830
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46092
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870092
  j =  1                              :        399907818
  j =  2                              :            46088
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:28.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:16.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:59.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.19e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.08e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.032
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.35
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.60
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.61
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.18
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.23
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.90
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9915

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17404.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.41
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.73
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.62
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.52
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.03
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.47
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.59
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.26
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.07
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.22
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.61
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.87
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.31
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.43
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.13
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  559.24
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.99
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.72
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.94
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.69
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4832.42
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.31
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.67
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.99
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.71
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5105.56
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.82
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.77
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    2.55
p-value of test                       :  5.4e-3



-----------------------------------------------
CPU time used                    :  00:02:22.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.60
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:24.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.12
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.94
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.94
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:05.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.61
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10159.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9705.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.067
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:04:14.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4980.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5024.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:52.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.48
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4264.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11738.94
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:30.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11984.10
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.47
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000037678

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.23
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000007561

Normal statistic for number of bits   :   0.060
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:01.95

 All tests were passed




Server wird beendet - Lösche Semaphor 116981766.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5336
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:57.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:42.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:43.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:05.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:57.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:02.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     543
p-value of test                       :    0.9903

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    2.37
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:11.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:45.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.87
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.89
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.10
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.80
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  192.48
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:44.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1512.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:02.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7041.52
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.23
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:04.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.55
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.85
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:32.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5094.75
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:11.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:52.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45806
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869806
  j =  1                              :        399908392
  j =  2                              :            45798
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45598
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869598
  j =  1                              :        399908809
  j =  2                              :            45588
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:26.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:16.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.77e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.049
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.34
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.98
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:48.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.83
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.51
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:37.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.70
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.62
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17443.08
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.89
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.47
p-value of test                       :    0.9902


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.88
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.91
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.11
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.19
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.66
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.25
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.32
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.56
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.81
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.12
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.01
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.21
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.06
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.51
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.38
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.16
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.59
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.38
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.11
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  318.46
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.56
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.82
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.61
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.32
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.75
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.06
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.10
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    2.28
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:02:22.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.00
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    1.38
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:23.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.79
p-value of test                       :    0.04

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.73
p-value of test                       :    0.96

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.28e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.81e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.37
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.11
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.16
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:06.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9958

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.37
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9875.85
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:40.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.62
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.79
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.37
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.35
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11506.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.46
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.48
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000057028

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.67
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000059176

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :  7.8e-4    *****

Anderson-Darling statistic = A2       :    4.53
p-value of test                       :  5.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.69
p-value of test                       :  3.5e-3

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:59.29

 All tests were passed




Server wird beendet - Lösche Semaphor 118063110.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997403
  j =  2                              :             1297
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1472
p-value of test                       :  2.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334592
  j =  1                              :        599997056
  j =  2                              :             1472
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5379
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:58.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:44.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:44.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:01.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:59.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:06.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:10.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:02.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:05.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:51.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:14.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:43.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.62
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.20
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.66
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.22
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.92
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.85
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.30
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:07.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7008.07
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.55
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.94
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:06.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.68
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4897.88
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:56.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46086
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870086
  j =  1                              :        399907830
  j =  2                              :            46082
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46064
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870064
  j =  1                              :        399907877
  j =  2                              :            46054
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:28.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:17.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:59.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.46e-6
p-value of test                       :    0.9995    *****

Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.77e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.91e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.029
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:42.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:43.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.99
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.03
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.47
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.96
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.49
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.73
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17705.06
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.40
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.33
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.64
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.76
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.05
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.29
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.62
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.46
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.10
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.25
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.34
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.58
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.71
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.42
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.33
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.07
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.97
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.96
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.76
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.71
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.85
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.49
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.14
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.15
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.53
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.83
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.21
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.84
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.55
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.33
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.85
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:22.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.07
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :    1.55
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:23.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 6.15e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.84e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.17
p-value of test                       :    0.9969

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.96
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.17
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:05.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.79e-3
p-value of test                       :    0.9928

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:05.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10148.78
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9894.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.033
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:04:14.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.86
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:52.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4991.15
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:53.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3882.47
p-value of test                       :    0.9957

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11611.70
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11761.29
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:31.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.87
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999997652

Normal statistic for number of bits   :  -0.019
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.38
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999919256

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:20.29

 All tests were passed




Server wird beendet - Lösche Semaphor 119046150.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5311
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:56.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7136
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:42.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4232
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7503
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:08.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:06.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:56.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:01.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:50.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    4.38
p-value of test                       :  5.7e-3

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:16.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:46.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.73
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.54
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.52
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.67
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.86
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1495.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:02.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6898.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:43.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.82
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:02.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.99
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.94
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:35.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4830.51
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:56.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908070
  j =  2                              :            45959
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45997
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869997
  j =  1                              :        399908011
  j =  2                              :            45987
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:25.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:17.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:53.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.15e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.032
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:35.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.59
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.46
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.62
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.49
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.86
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17465.31
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.83
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.22
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.25
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.98
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.56
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.86
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.81
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.84
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.98
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.90
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.43
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.41
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.29
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.45
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.40
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.51
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.29
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.21
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.20
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.68
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.75
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.38
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.68
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.07
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.06
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.41
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.89
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.85
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.26
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.94
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:23.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.88
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:22.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.77e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 4.56e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.65
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.48
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.97
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:04.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.53
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:06.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    5.00
p-value of test                       :  3.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9588.46
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10074.75
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:45.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5053.22
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4188.21
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.48
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11719.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   82.21
p-value of test                       :  8.0e-3


-----------------------------------------------
Total number of bits:  7999850487

Normal statistic for number of bits   :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.34
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999928046

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   0.093
p-value of test                       :    0.46

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:18.37

 All tests were passed




Server wird beendet - Lösche Semaphor 120094726.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5320
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:01.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:44.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:01.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:12.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7156
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:08.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:12.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     558
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:14.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:41.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.35
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.28
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.90
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  188.91
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:54.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.57
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:06.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6894.20
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.19
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.94
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:16.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.46
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   80.63
p-value of test                       :    0.9972


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4914.94
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:54.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46043
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870043
  j =  1                              :        399907918
  j =  2                              :            46035
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45996
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869996
  j =  1                              :        399908011
  j =  2                              :            45990
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:28.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:17.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:04.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:56.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:39.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.63e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.04e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 9.03e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.37
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:00:24.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    3.08
p-value of test                       :  1.0e-3

-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.77
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.40
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.85
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.33
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:52.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.90
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.82
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.50
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17736.36
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.71
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.83
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.17
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.74
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.74
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.57
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.79
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.42
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.31
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.93
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.77
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.13
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  439.41
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.78
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.45
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.14
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.27
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.03
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.17
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.45
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.05
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.73
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.81
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.22
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.07
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.55
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.61
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.25
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.99
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.62
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.32
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    1.64
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:23.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.88
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -1.78
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:23.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 9.55e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.18e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.16e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.54
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.03
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:04.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.72
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:03.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9867.12
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.097
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:04:24.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:53.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.91
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:51.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.74
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11786.22
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11934.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:30.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.75
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000000328

Normal statistic for number of bits   : 2.59e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.70
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000075355

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:13.29

 All tests were passed




Server wird beendet - Lösche Semaphor 121110534.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5505
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:42.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:35.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:34.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7075
p-value of test                       :    0.9978


-----------------------------------------------
CPU time used                    :  00:02:59.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:59.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:51.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:57.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    2.87
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     829
p-value of test                       :    0.9913

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:51.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     647
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:09.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.52
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:33.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.61
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.14
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.69
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.86
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.95
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.60
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  163.18
p-value of test                       :    0.9998    *****

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.17
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.28
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:02.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7133.89
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.20
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.34
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:02.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.19
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.22
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4894.50
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:15.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45943
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869943
  j =  1                              :        399908117
  j =  2                              :            45937
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45596
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869596
  j =  1                              :        399908811
  j =  2                              :            45590
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:28.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:16.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 2.17e-3
p-value of test                       :    0.9977

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:43.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 3.08e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 7.19e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.055
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.084
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.08
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.18
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.91
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.91
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:32.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 1.20e-3
p-value of test                       :    0.9988

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   92.24
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17396.74
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.36
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.61
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.58
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.85
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.07
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.25
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.78
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.93
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.37
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.26
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.91
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.17
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.29
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.90
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.31
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.55
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.76
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.72
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.78
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.97
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:47.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.00
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.82
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.85
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.33
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  158.40
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.13
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.08
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.28
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.82
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.44
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.25
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:13.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.26
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    0.86
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:12.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.2e-3

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.91
p-value of test                       :    0.03

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:46.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.89e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.09
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.01
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.11
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:09.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.83
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:10.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10044.53
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9889.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:45.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.77
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.34
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4220.60
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11603.61
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11679.48
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.15
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000042328

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.48
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000124897

Normal statistic for number of bits   :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.2e-3

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.28
p-value of test                       :    0.01

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   0.035
p-value of test                       :    0.49

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:14:55.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 34  Gap, r = 0                      0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 101810183.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997413
  j =  2                              :             1292
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:43.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:37.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:35.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:03.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:59.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:03.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    2.91
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     676
p-value of test                       :  1.2e-3

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    3.52
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:04.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    2.83
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:38.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.37
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.94
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.51
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.56
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.72
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  197.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.72
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.68
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:06.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7005.66
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:56.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.13
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:17.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.91
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.55
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5171.28
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:15.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46161
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870161
  j =  1                              :        399907681
  j =  2                              :            46155
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45826
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869826
  j =  1                              :        399908349
  j =  2                              :            45824
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:29.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:16.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:43.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:54.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :  1.3e-3

Anderson-Darling statistic = A2       :    4.03
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.40e-4
p-value of test                       :  9.9e-3

Kolmogorov-Smirnov- statistic = D-    : 5.24e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.88e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.38e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.49
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.29
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.51
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.21
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.54
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:51.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.65
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.82
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.07
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17472.75
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.23
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.57
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.72
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.25
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.90
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.25
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.02
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.26
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.83
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.49
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.04
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.52
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.89
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.81
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.39
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.84
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.98
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.78
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.43
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.56
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.43
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.82
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.89
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.13
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.90
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.30
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4938.67
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.73
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.26
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.54
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:26.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.62
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    1.65
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:28.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         : -5.43e-3
p-value of test                       :    0.50

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 5.18e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.26e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.61
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.16
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.42
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:06.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.23
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10219.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10126.00
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:04:27.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.90
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:55.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.91
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:58.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.75
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11949.03
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:33.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11997.78
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.76
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000099622

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.24
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000000646

Normal statistic for number of bits   : 5.11e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:14:15.53

 All tests were passed




Server wird beendet - Lösche Semaphor 103153671.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:46.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:46.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:37.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:37.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:55.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:02.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:02.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:51.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:00.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.88
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:16.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:44.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.41
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.53
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.94
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.35
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.96
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  194.37
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.69
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.34
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7049.92
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:44.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.30
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.69
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:02.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.28
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.55
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:34.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5097.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:58.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45744
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869744
  j =  1                              :        399908516
  j =  2                              :            45736
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45981
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869981
  j =  1                              :        399908043
  j =  2                              :            45971
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:24.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:16.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:54.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :  1.8e-3

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 3.44e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.052
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:30.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.59
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.21
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.19
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.81
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:44.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:29.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.25
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17327.29
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.34
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.64
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.87
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.35
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.61
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.21
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.83
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.26
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.46
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.47
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.76
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.86
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.94
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.55
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.55
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.25
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.77
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.22
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.11
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.70
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.09
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.45
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.34
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.42
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.91
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.20
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.35
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.26
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:23.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.16
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -2.02
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:22.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.78e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.51
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.58
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.88
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.14
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:07.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9947

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.40
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:43.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.86
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.05
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4228.18
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.74
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.77
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999865883

Normal statistic for number of bits   :   -1.06
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.33
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999905342

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.46
p-value of test                       :  6.9e-3

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:37.54

 All tests were passed




Server wird beendet - Lösche Semaphor 104529927.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:48.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:38.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:37.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:55.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:02.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:01.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:52.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:01.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:15.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.15
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:44.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.22
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    5.45
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.89
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.81
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.11
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.95
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.71
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7092.92
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.01
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:02.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.06
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.19
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:33.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4996.07
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:57.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45641
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869641
  j =  1                              :        399908720
  j =  2                              :            45637
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908479
  j =  2                              :            45753
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:25.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:16.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:00.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.94e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9976

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.035
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:31.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.79
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.14
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.54
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.27
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.54
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.48
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.46
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  164.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17625.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.13
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.55
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.37
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.86
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.27
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.74
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.45
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.33
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.47
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.19
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.19
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.43
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.22
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.99
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.12
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  428.78
p-value of test                       :    0.9906


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.89
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.63
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.65
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.58
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.92
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.50
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.54
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.18
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.94
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5069.66
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  320.89
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.64
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.67
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:26.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.60
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    1.51
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.52e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.92e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.34
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.76
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.31
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.54
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:08.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.20
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.28
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.029
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:41.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.80
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.38
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3972.59
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11861.68
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12084.29
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.38
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000066862

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.35
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000159535

Normal statistic for number of bits   :    1.26
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.90
p-value of test                       :    0.03

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:54.68

 All tests were passed




Server wird beendet - Lösche Semaphor 105283591.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5478
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:46.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:38.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:36.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4212
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:02.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:02.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:52.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:01.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.85
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:13.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:02:43.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   19.76
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.39
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.09
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.97
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.76
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  281.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7111.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:43.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.53
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.74
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:18.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.48
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.52
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:33.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5108.99
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:02.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45519
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869519
  j =  1                              :        399908967
  j =  2                              :            45509
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45645
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869645
  j =  1                              :        399908713
  j =  2                              :            45639
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.93e-3
p-value of test                       :    0.9954

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:27.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:18.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:45.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:54.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.53e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 5.38e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.69
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.13
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.68
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.05
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.79
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.08
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.51
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.03
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.05
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17391.75
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.00
p-value of test                       :    0.9911


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.98
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.58
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.14
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.22
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.93
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.82
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.78
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.93
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.01
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.10
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.00
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.61
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.90
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.77
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.06
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.42
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.12
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.72
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.53
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.34
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.80
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.12
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.53
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.40
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.92
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.92
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.53
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.56
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.80
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.66
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:21.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.47
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:21.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 6.44e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.20
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.15
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.06
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:07.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:06.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9751.16
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.57
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.055
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.088
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:46.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4816.70
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.01
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:50.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4269.36
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4004.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11597.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11643.92
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.56
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999874625

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.98
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999976631

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:53.29

 All tests were passed




Server wird beendet - Lösche Semaphor 106233863.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5487
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:49.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4218
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:38.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:38.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:02.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:01.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:51.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:00.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:13.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:43.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.73
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.79
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.64
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.00
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.59
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.17
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:00.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7072.53
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:41.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.04
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:02.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.21
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.72
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5203.90
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:57.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46060
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870060
  j =  1                              :        399907881
  j =  2                              :            46058
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46105
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870105
  j =  1                              :        399907794
  j =  2                              :            46097
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:26.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:17.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:44.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:33.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.14e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 2.79e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:35.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.80
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.22
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.57
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.75
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.03
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.58
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17430.81
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.39
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.66
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.45
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.44
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.48
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.12
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.91
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.18
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.20
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.39
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.72
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.47
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.34
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.28
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.05
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.84
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.85
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.47
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.99
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.93
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.02
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.94
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.59
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.77
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.51
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.56
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4820.93
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.38
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.12
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:23.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.41
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -1.20
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:22.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.20
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.50e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.08e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.44
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.06
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.95
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:07.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9967.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.67
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:45.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4724.45
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.31
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.92
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.39
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.53
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.75
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.86
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999923537

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.87
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000092686

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.19
p-value of test                       :    0.99

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    2.53
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:29.35

 All tests were passed




Server wird beendet - Lösche Semaphor 107118599.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9933


-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5502
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:53.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:56.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:58.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:03.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7492
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:52.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:59.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.98
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    2.28
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:11.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.43
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    3.42
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     120
p-value of test                       :    0.9934

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:45.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.59
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.64
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.57
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.70
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.91
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.90
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.40
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1289.34
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:02:01.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6868.09
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.89
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:00.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.26
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.21
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:30.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5117.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9942


-----------------------------------------------
CPU time used                    :  00:03:02.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45773
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869773
  j =  1                              :        399908462
  j =  2                              :            45757
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908146
  j =  2                              :            45921
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:27.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:18.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:54.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:33.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 8.67e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.73e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:33.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.46
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.17
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.05
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.56
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.80
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:40.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.82
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.96
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17516.92
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.83
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.97
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.54
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.99
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.05
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.13
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.02
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.16
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.25
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.74
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.43
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.37
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.97
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.09
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.02
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.78
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.13
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.19
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.50
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.61
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5189.87
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.29
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.50
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.68
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.61
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5147.14
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.25
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.68
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.38
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:21.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.67
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:21.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.26e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.94e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.49
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.45
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:05.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.99
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:05.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9758.22
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10243.38
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.036
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:42.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4674.93
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:47.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.48
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:49.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4226.62
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.32
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11949.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12099.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.19
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000095464

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.01
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000270931

Normal statistic for number of bits   :    2.14
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.12

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   0.091
p-value of test                       :    0.46

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:53.06

 All tests were passed




Server wird beendet - Lösche Semaphor 108068871.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5473
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:55.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:39.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4200
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4458
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:03.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:04.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:54.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7469
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:59.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.79
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:11.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    3.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:42.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.81
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.81
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.45
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.55
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.62
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.99
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.91
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  503.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1359.18
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7157.33
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:42.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.83e-3
p-value of test                       :    0.9930

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.80
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:02.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.38
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.40
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4987.74
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:04.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45624
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869624
  j =  1                              :        399908754
  j =  2                              :            45620
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46231
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870231
  j =  1                              :        399907542
  j =  2                              :            46223
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.46e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  7.7e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:28.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:18.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.53e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:01.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:33.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.055
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:34.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.22
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.92
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.10
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.89
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.70
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:37.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.24
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.37
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.99e-3
p-value of test                       :    0.9959

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  171.99
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17640.30
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.46
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.33
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.77
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.53
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.08
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.75
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.72
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.23
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.48
p-value of test                       :    0.9961


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.32
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.11
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.79
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.85
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.71
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.04
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.92
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.25
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.92
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.33
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.61
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.53
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.41
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.79
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.60
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.63
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.02
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.44
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.41
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.54
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.82
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    1.42
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:22.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.69
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:22.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.22e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 9.11e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.35e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.53
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.23
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:05.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.26
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.13
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.14
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:41.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.76
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.44
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3976.08
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.02
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11824.95
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:29.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.40
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999907775

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.80
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000105715

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:23.50

 All tests were passed




Server wird beendet - Lösche Semaphor 109019143.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5324
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:40.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7507
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:03.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:03.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:53.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:59.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.42
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9968

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:10.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.64
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.92
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.52
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.43
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.87
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  470.70
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1520.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:00.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6881.26
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:02.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.99
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.01
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:32.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5026.17
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:03.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45859
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869859
  j =  1                              :        399908287
  j =  2                              :            45849
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45671
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869671
  j =  1                              :        399908664
  j =  2                              :            45659
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:27.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:18.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  4.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    4.04
p-value of test                       :  8.5e-3


-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.13e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.93e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.071
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:30.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:31.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.80
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.29
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.56
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:38.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.77
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.22
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17305.07
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.58
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.09
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.00
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.15
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.32
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.91
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.23
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.92
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.17
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.41
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.44
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.82
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.82
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.15
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.33
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.26
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.57
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.42
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.85
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.99
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.45
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.62
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.89
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.27
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.45
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.38
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.85
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :    1.41
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.19
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9939

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.21e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 4.87e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.52
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.78
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:04.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.52
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9717.36
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9803.18
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:40.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5147.46
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4991.95
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4198.69
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12015.35
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12213.82
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.47
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999950093

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.73
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000078295

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:07.04

 All tests were passed




Server wird beendet - Lösche Semaphor 109936647.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5404
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:54.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7515
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:04.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7497
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:05.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:53.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:58.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    2.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:45.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    4.16
p-value of test                       :  7.3e-3

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:10.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.85
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:41.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.32
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.90
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.99
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.95
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.09
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:45.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1376.89
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7086.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.87
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.85
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:02.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.69
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4892.12
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:01.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45603
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869603
  j =  1                              :        399908797
  j =  2                              :            45597
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45685
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869685
  j =  1                              :        399908634
  j =  2                              :            45677
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:28.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:33.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 2.78e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.85e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 3.17e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:32.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:33.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.93
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.11
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.40
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.82
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.23
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.60
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:37.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.86
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.15
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9953

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.75
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17666.36
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.55
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.73
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.52
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.72
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.57
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.46
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.66
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.78
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   47.52
p-value of test                       :  2.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.00
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.78
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.05
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.36
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.98
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.84
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.90
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.69
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.81
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.81
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.48
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.77
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4904.14
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.71
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.85
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.65
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5115.56
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.05
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.18
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.00
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -0.98
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:22.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.79
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:23.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.63e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 9.62e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.72e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.12
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.47
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.10
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:05.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10062.49
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.50
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9667.65
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.041
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:42.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.14
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.7e-3

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4998.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4008.96
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.64
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11921.28
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.25
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.69
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999969767

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.00
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000002458

Normal statistic for number of bits   :   0.019
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :  -0.035
p-value of test                       :    0.51

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:14.47

 All tests were passed




Server wird beendet - Lösche Semaphor 110886919.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9937


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5593
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:53.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:40.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:05.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7169
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:54.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:59.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:46.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:13.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:40.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.12
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.92
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.26
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.89
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.77
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.28
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.82
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6944.70
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.45
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:01.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.30
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.32
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:34.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4963.96
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:11.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45674
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869674
  j =  1                              :        399908656
  j =  2                              :            45666
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46237
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870237
  j =  1                              :        399907529
  j =  2                              :            46231
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:27.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.35e-3
p-value of test                       :    0.9975

Anderson-Darling statistic = A2       :    4.46
p-value of test                       :  5.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9988


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:19.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:01.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:33.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.29e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:33.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:48.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.96
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.80
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.88
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.07
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:38.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.30
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.79
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.12
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17190.37
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.22
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.61
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.08
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.42
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.53
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.34
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.40
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.76
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.21
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.29
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.92
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.93
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.08
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.86
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.16
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.86
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  423.19
p-value of test                       :    0.9945


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.98
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.08
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.84
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.55
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.87
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.87
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.70
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.60
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.61
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.40
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.76
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.86
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.07
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:22.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.57
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:22.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.86e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 6.74e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 4.33e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.96
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.38
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.73
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:05.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9868.89
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9933.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.059
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:39.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.61
p-value of test                       :  4.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5187.87
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.59
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.32
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11887.86
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12000.28
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.56
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000220216

Normal statistic for number of bits   :    1.74
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.02
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000047014

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.28
p-value of test                       :    0.99

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:27.50

 All tests were passed




Server wird beendet - Lösche Semaphor 111902727.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997373
  j =  2                              :             1312
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5511
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:55.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:57.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:05.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:06.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:58.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    2.53
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:14.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:42.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   19.66
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.03
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.95
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.27
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.04
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.89
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.12
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1544.53
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:01.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6979.09
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.96
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:05.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.55
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.06
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:32.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5198.52
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:05.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45750
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869750
  j =  1                              :        399908501
  j =  2                              :            45748
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45853
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869853
  j =  1                              :        399908299
  j =  2                              :            45843
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:27.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.85e-3
p-value of test                       :    0.9931

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:01.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:54.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:33.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 9.46e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.12e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:33.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:34.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.86
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.33
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.79
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.31
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.02
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:38.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.56
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.40
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17550.67
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.63
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.82
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.69
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.98
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.02
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.94
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.77
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.05
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.73
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.05
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.06
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.22
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.96
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.52
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.80
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.26
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.24
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.01
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.50
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.11
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.15
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.93
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5133.62
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.78
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.26
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.55
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.73
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.88
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.70
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.10
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.49
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:23.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.10
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -2.96
p-value of test                       :    0.9984



-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.18e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.41e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 8.85e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.75
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.65
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.09
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:07.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.89
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:06.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10030.98
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10064.21
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.032
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:39.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.25
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4712.56
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.05
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11575.47
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11824.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.15
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000116872

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.05
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000150991

Normal statistic for number of bits   :    1.19
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.018
p-value of test                       :    0.49

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:00.97

 All tests were passed




Server wird beendet - Lösche Semaphor 112885767.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1266
p-value of test                       :    0.9963

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334386
  j =  1                              :        599997468
  j =  2                              :             1266
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5411
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:56.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:41.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:05.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7077
p-value of test                       :    0.9977


-----------------------------------------------
CPU time used                    :  00:03:05.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:56.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:59.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.43
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    3.31
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     545
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.31
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:15.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    2.61
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.37
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.25
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.03
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.85
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.61
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.43
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.73
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1508.85
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6976.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:02.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.27
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.23
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5010.28
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:05.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46190
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870190
  j =  1                              :        399907625
  j =  2                              :            46180
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45969
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869969
  j =  1                              :        399908065
  j =  2                              :            45963
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:27.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:17.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:45.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:00.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:41.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.70e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 5.32e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:33.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.86
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.19
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.21
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.46
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.78
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:37.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.44
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.60
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.29
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.44
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.17
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17367.11
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.75
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.38
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.07
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.25
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.58
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.89
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.84
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.07
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.84
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.49
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.84
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.65
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.56
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.47
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.63
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.84
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.90
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.97
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.36
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.85
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5134.92
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.46
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.17
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.98
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.95
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.63
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  433.59
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.54
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:34.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.76
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.11
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:23.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    2.68
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.28e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.92e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 9.73e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.84
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.25
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.55
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.02
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9931.51
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.92
p-value of test                       :  1.8e-3

-----------------------------------------------
CPU time used                    :  00:03:40.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.74
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:47.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4778.01
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:48.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.81
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.80
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11615.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11844.83
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.40
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999983543

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.63
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999976649

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.92

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   0.014
p-value of test                       :    0.49

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:03.96

 All tests were passed




Server wird beendet - Lösche Semaphor 113901575.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:48.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1476
p-value of test                       :  1.5e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334596
  j =  1                              :        599997048
  j =  2                              :             1476
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1256
p-value of test                       :    0.9984

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334376
  j =  1                              :        599997488
  j =  2                              :             1256
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5411
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:54.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4128
p-value of test                       :    0.9993    *****


-----------------------------------------------
CPU time used                    :  00:01:59.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:08.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:09.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:01.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:02.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    2.15
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.04
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.45
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:14.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:44.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.95
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.84
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.03
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.22
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.84
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.15
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.28
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  485.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.48
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6920.68
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.55
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.18
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:07.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.15
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.86
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:36.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4995.83
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:12.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45922
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869922
  j =  1                              :        399908158
  j =  2                              :            45918
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46101
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870101
  j =  1                              :        399907800
  j =  2                              :            46097
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9953

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:29.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 2.85e-3
p-value of test                       :    0.9969

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:44.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:01.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:55.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:36.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.63e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 2.43e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.03e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:42.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.55
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.26
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.14
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.07
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.12
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.18
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.46
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.65
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17367.71
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.10
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.52
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.64
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.09
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.10
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.77
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.99
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.74
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.91
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.21
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.04
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.12
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.72
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.79
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  102.62
p-value of test                       :    0.9975


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.08
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.94
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.98
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.71
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.50
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.06
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.20
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.36
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  467.84
p-value of test                       :  2.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.03
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.55
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.90
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.95
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -1.21
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:23.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.69
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:24.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 9.13e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.26e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.35
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.46
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:06.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.17
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:06.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9894.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : 4.72e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:04:14.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4698.21
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:52.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4711.10
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:53.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.64
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.10
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:31.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11873.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.76
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999992051

Normal statistic for number of bits   :  -0.063
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   26.88
p-value of test                       :    0.9993    *****


-----------------------------------------------
Total number of bits:  7999968156

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:22.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 17  BirthdaySpacings, t = 7         0.9993 
 102  Run of bits, r = 27             0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 114917383.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:57.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:43.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:44.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:01.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:10.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:09.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:12.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9941

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    2.06
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:14.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.15
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.08
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.06
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.52
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.10
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.23
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.47
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.54
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.88
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.91
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:08.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6958.01
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:57.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.37
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.78
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.47
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:13.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.06
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.36
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4992.59
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46058
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870058
  j =  1                              :        399907889
  j =  2                              :            46048
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45843
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869843
  j =  1                              :        399908317
  j =  2                              :            45837
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:28.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:09.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:57.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:39.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.18e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:24.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:52.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.73
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.69
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.34
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.16
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:53.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.59
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.88
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.92
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17593.93
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.06
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.45
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.29
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.26
p-value of test                       :  7.8e-3


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.15
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.21
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.73
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.39
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.09
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.73
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.51
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.17
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.75
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.89
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.80
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.47
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.47
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.11
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.58
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.05
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.59
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.04
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.67
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.95
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.51
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.00
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.89
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  435.56
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.00
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.12
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:22.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.03
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:22.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.49e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 9.82e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 8.85e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.67
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.13
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:38.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.36
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.65
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:23.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10049.91
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : -3.52e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:04:37.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.20
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:54.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.92
p-value of test                       :  1.0e-2

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4668.81
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.10
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.44
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11696.95
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:33.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11675.29
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:34.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.46
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999811202

Normal statistic for number of bits   :   -1.49
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.22
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999864359

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:37.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.88

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:37.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:33.04

 All tests were passed




Server wird beendet - Lösche Semaphor 116031495.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1487
p-value of test                       :  5.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334607
  j =  1                              :        599997026
  j =  2                              :             1487
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:56.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:43.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:01.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:10.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:09.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:56.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    2.02
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     335
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:11.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    2.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:40.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.56
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.72
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.85
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.26
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.52
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.42
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  378.58
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:27.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1513.23
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:14.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7031.03
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:31.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.67
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:06.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.84
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.99
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5121.40
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:57.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45635
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869635
  j =  1                              :        399908734
  j =  2                              :            45627
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45793
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869793
  j =  1                              :        399908420
  j =  2                              :            45781
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.67
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  4.6e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:27.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:18.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:45.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:35.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.97e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:34.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:37.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.82
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.86
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.64
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.88
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.11
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:02.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.38
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.13
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.14
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.71
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17583.19
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.55
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.14
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.45
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.87
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.32
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.88
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.46
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.43
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.17
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  206.53
p-value of test                       :  7.3e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.69
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  441.79
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.27
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.63
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.57
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.50
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.99
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.18
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.99
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.90
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.17
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.94
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.24
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.37
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.15
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  444.98
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.45
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.44
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.01
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.85
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.46
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:22.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 4.72e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.43e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 5.34e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.26
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.96
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.23
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:04.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.34
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:05.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10280.52
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9871.46
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:42.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.58e-3
p-value of test                       :    0.9919

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5103.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.59
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.51
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4226.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11978.24
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11950.66
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.40
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000073891

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.85
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000151522

Normal statistic for number of bits   :    1.20
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.44
p-value of test                       :    0.07

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:04.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           5.4e-4
 76  RandomWalk1 H (L=1000, r=0)     7.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 117243911.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5505
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:55.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:42.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:59.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:07.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:07.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7108
p-value of test                       :    0.9931


-----------------------------------------------
CPU time used                    :  00:03:58.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:04.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9925

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:12.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    2.91
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:40.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.42
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.33
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.77
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.70
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.63
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:05.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7022.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.12
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.03
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:07.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.99
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.92
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:36.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5131.62
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:59.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45982
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869982
  j =  1                              :        399908042
  j =  2                              :            45970
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45555
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869555
  j =  1                              :        399908895
  j =  2                              :            45545
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:30.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:18.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:02.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.40e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.050
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:43.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.64
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.20
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.50
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.52
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.55
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.72
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.92
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.86
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.12
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.77
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17224.81
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.33
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.72
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.28
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.07
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.48
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.49
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.39
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.04
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.33
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.19
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.54
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.72
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.01
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.61
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.45
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.83
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.00
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.69
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.58
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.86
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5150.60
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.64
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.33
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.06
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.66
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.41
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.21
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.71
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.55
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:24.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.14
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    1.73
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:22.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.77e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.78e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.84
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.75
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.69
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:03.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.91
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:04.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10043.55
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.62
p-value of test                       :  4.4e-3

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:04:11.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.36
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:53.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:53.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.20
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.20
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11652.94
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:30.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.39
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000046192

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   83.70
p-value of test                       :  5.9e-3


-----------------------------------------------
Total number of bits:  8000067291

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:29.18

 All tests were passed




Server wird beendet - Lösche Semaphor 118226951.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1493
p-value of test                       :  3.1e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334613
  j =  1                              :        599997014
  j =  2                              :             1493
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:56.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:43.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:42.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:59.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:07.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:10.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:04.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:04.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.26
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:13.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:42.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.60
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.59
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.50
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.84
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.50
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.16
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1467.31
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7061.17
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:54.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.61
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.31
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:27.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.48
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.00
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:37.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5159.16
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:57.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45255
p-value of test                       :    0.9982


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869255
  j =  1                              :        399909493
  j =  2                              :            45249
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46519
p-value of test                       :  1.5e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870519
  j =  1                              :        399906967
  j =  2                              :            46509
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:31.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:19.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:03.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.01e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.14e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.57e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:41.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.93
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.74
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   61.10
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.25
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.44
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.10
p-value of test                       :    0.9917

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.11
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.67
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17283.80
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.65
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.45
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.11
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.03
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.11
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.81
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.12
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.95
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.59
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.81
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.54
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.51
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.27
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.35
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.70
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.07
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.91
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.98
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.98
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.93
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.75
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5104.98
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  433.58
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.81
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.64
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  444.44
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.85
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.19
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  241.35
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.79
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   0.034
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:21.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.60
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :  -0.051
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:22.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 3.89e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.56e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.18
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.12
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.40
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:04.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:04.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10205.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.11
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:04:16.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.44
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:52.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4756.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:57.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.86
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:33.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11509.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:34.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.22
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999956333

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.13
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000153916

Normal statistic for number of bits   :    1.22
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:41.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           3.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 119341063.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:06.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:55.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:00.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.36
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:13.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:43.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.21
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.92
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.12
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.74
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.28
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.81
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  191.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.92
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:03.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7263.32
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:46.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.89
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:02.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.36
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.84
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4977.41
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:59.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45431
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869431
  j =  1                              :        399909144
  j =  2                              :            45419
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46057
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870057
  j =  1                              :        399907891
  j =  2                              :            46047
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  7.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.82
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9901


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:28.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:18.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:59.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:34.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.62e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.24
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:48.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.02
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.98
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.01
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.78
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.50
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17768.42
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.35
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.73
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.50
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.30
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.85
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.94
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.53
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.47
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.57
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.31
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.42
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.02
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.52
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.26
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.83
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.76
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.58
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.97
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.73
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.99
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.94
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4857.30
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.88
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.84
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.39
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.03
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.93
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  324.69
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.16
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.17
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:21.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.50
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:22.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9923

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.73e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.36
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.51
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.52
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:03.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.94
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.49
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:39.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.70
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4775.91
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:48.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.69
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11831.42
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12008.71
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.46
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000012478

Normal statistic for number of bits   :   0.099
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   82.63
p-value of test                       :  7.3e-3


-----------------------------------------------
Total number of bits:  7999909296

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:49.37

 All tests were passed




Server wird beendet - Lösche Semaphor 120389639.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1493
p-value of test                       :  3.1e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334613
  j =  1                              :        599997014
  j =  2                              :             1493
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:55.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4450
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:39.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:05.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:56.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:00.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.39
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    2.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:12.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:41.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.26
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.60
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.40
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.65
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.44
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.56
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.97
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.58
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1363.77
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:04.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6966.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:44.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.05
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.12e-3
p-value of test                       :    0.9946

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:04.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.09
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.47
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:35.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5206.63
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:00.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45849
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869849
  j =  1                              :        399908304
  j =  2                              :            45845
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45426
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869426
  j =  1                              :        399909150
  j =  2                              :            45422
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  1.8e-3

Anderson-Darling statistic = A2       :    5.25
p-value of test                       :  2.2e-3


-----------------------------------------------
CPU time used                    :  00:02:28.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:18.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:33.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.28e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.83e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:35.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:35.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.84
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.31
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.18
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.56
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.81
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.45
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   14.73
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17229.72
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.00
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.26
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.43
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.86
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.72
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.14
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.65
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.50
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.74
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.78
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.84
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  599.08
p-value of test                       :  1.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.27
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.78
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.49
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.13
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.85
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.38
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  110.25
p-value of test                       :  4.0e-3


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  455.61
p-value of test                       :  6.9e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  294.85
p-value of test                       :    0.9998    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.00
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  444.60
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.02
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.71
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.72
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.73
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.54
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.73
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :  -0.051
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:19.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.53
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -1.88
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:19.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.58
p-value of test                       :  5.0e-3

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.53e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 5.65e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.52e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.43
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.25
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.64
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.99
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:58.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10162.91
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.68
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:51.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:22.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.65e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5050.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.06
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:31.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.74
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4023.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11823.19
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11947.03
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.24
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000059200

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.82
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000154714

Normal statistic for number of bits   :    1.22
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.079
p-value of test                       :    0.47

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:59:08.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           3.1e-4
 78  RandomWalk1 M (L=10000, r=0)    0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 121372679.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:41.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:35.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:33.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:54.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:01.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:01.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:51.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:56.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.53
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:10.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    2.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:35.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.69
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.92
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.93
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.98
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.95
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.22
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.72
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.96
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:03.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7001.83
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.80
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.48
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:07.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.84
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:35.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4931.83
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45812
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869812
  j =  1                              :        399908380
  j =  2                              :            45804
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45948
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869948
  j =  1                              :        399908107
  j =  2                              :            45942
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  8.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:28.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:17.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:44.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:57.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:53.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.09e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:34.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.09
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.54
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:10.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.23
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.34
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:33.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:32.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17170.35
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.04
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.32
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.87
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.77
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.39
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:39.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.99
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.81
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.09
p-value of test                       :    0.9974


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.55
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.39
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.84
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.60
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  171.99
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  106.74
p-value of test                       :  7.6e-3


-----------------------------------------------
CPU time used                    :  00:00:47.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.48
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.95
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.34
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.71
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:47.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.38
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.58
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5174.78
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.42
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.56
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.30
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.64
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  319.17
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.37
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.21
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.54
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:12.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.49e-3
p-value of test                       :    0.9964

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.13e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.16e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 8.72e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.20
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.34
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.21
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:08.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:11.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10123.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.54
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:45.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4933.77
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.10
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.58
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.70
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11801.94
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11610.61
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.69
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000153433

Normal statistic for number of bits   :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.71
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000060067

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:14:50.26

 All tests were passed




Server wird beendet - Lösche Semaphor 101842952.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:51.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:41.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:36.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:34.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:53.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:53.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:00.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:01.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:52.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:57.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.27
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    4.25
p-value of test                       :  6.6e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     678
p-value of test                       :  9.5e-4    *****

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:12.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:38.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.59
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.53
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.14
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.04
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.66
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.71
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  391.27
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:49.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1387.02
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6886.95
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.91
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.60
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:02.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.21
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.31
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:35.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5020.11
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:12.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45747
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869747
  j =  1                              :        399908508
  j =  2                              :            45743
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45578
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869578
  j =  1                              :        399908847
  j =  2                              :            45572
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:29.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:19.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:45.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:53.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.66e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:36.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.86
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:48.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.00
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.40
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.72
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.66
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.080
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17552.44
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.58
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.48
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.52
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.76
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.92
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.84
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.60
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.50
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.78
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:40.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.32
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.13
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.49
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.11
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.25
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:47.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.90
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.28
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.80
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.93
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.44
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.04
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.84
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.50
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.94
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.72
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5224.87
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.24
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.41
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:18.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.28
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:15.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.36e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.14
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.99
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.13
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:06.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:10.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10181.18
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.05
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.074
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:46.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.37
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.12
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4046.50
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.98
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11818.51
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11535.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.13
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999913778

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.28
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999923351

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:11.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs NJumps, t = 5        9.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 102793224.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5477
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:43.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:36.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:34.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:53.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:53.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:59.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:01.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:52.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:58.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.77
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:09.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:39.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.14
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.52
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.14
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.03
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.63
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.51
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.22
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.66
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.71
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:01.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7108.41
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.71
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:02.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:46.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.15
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:34.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4917.13
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:07.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45512
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869512
  j =  1                              :        399908979
  j =  2                              :            45506
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45696
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869696
  j =  1                              :        399908610
  j =  2                              :            45692
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:19.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:54.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.24e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.07e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:33.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.06
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.32
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.76
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.40
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.14
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:44.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.17
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.99
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   13.35
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.05
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.50
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17592.22
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.07
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.56
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.36
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.96
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.16
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.52
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.53
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.13
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.03
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.59
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.88
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.49
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.68
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.37
p-value of test                       :  9.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.33
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.36
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.15
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.18
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.67
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.86
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.32
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.98
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.82
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.50
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.44
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.53
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.04
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:33.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.73
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :    1.97
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:16.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.35
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:17.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.96

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.22e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.15
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.13
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.40e-3
p-value of test                       :    0.9954

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  157.85
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:08.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.84
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:07.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10035.86
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10141.62
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:46.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.31
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.71
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.19
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11977.22
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.25
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999942344

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.11
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999994907

Normal statistic for number of bits   :  -0.040
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:11.45

 All tests were passed




Server wird beendet - Lösche Semaphor 103972872.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:40.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:46.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:38.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:38.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:01.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:01.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:52.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:57.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     845
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:03.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.29
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    2.31
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.96
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:14.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.69
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.75
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.57
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.30
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.82
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.71
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.74
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.17
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.81
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:46.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:02.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7064.81
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.38
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:05.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.83
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.57
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:32.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5175.55
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:03.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46472
p-value of test                       :  2.9e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870472
  j =  1                              :        399907063
  j =  2                              :            46458
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45946
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869946
  j =  1                              :        399908109
  j =  2                              :            45944
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:29.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:25.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:53.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 2.99e-3
p-value of test                       :    0.9968

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:08.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:54.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.00e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:34.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:32.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.33
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.75
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.46
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.17
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:40.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.17
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.88
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.40
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17422.89
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.67
p-value of test                       :    0.9924


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.37
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.44
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.49
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.57
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.07
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.20
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.02
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.09
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.74
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.69
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  426.31
p-value of test                       :    0.9925


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.92
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.50
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.24
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.32
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.78
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.00
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.51
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5133.58
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.49
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.91
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.69
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.11
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5080.15
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.09
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.03
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.77
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:19.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.45
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -1.36
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:20.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.85
p-value of test                       :    0.03

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.88

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 8.74e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 8.11e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:47.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.04
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.40
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.13
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:05.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.09
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:08.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.28
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.44
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:04:30.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.57
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4770.90
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.03
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11752.01
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11899.96
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.90
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000121915

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.74
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999958457

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:09.29

 All tests were passed




Server wird beendet - Lösche Semaphor 105054216.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:50.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1473
p-value of test                       :  1.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334593
  j =  1                              :        599997054
  j =  2                              :             1473
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5496
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:51.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:38.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4182
p-value of test                       :    0.9907


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:00.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:01.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:51.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:57.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:01.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     557
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.44
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:14.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:43.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.28
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.57
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.45
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.40
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.71
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.73
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.44
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.99
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.42
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1406.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7059.30
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.63
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.11
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:02.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.07
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.05
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4957.44
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:01.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46277
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870277
  j =  1                              :        399907450
  j =  2                              :            46269
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46007
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870007
  j =  1                              :        399907989
  j =  2                              :            46001
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:28.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:25.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:08.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:33.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.32e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.20e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:31.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:33.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:48.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.37
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.29
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.21
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.64
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.75
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17274.42
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.28
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.07
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.08
p-value of test                       :    0.9926


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.89
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.83
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.98
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.08
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.43
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.26
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.34
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.20
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.55
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.30
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.85
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.96
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.41
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.13
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.47
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.54
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.03
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.76
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.43
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.09
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.96
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.86
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.99
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5088.34
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.25
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.61
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.54
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:18.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.99
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:20.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 3.83e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.98e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.43
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.97
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.66
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:06.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.88
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.38
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:04:32.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:47.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4737.89
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:49.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.25
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4204.26
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11963.62
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11523.93
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.97
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999909683

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.71
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999898673

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9925

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:55.34

 All tests were passed




Server wird beendet - Lösche Semaphor 105873416.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:50.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5495
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:52.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:39.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:03.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:02.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:52.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:57.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.55
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.21
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    6.35
p-value of test                       :  7.2e-4    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    2.12
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    2.16
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:10.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:38.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.58
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.09
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.58
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.58
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.59
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.75
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1441.67
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:01.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7084.57
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.73
p-value of test                       :  1.7e-3

Anderson-Darling statistic = A2       :    4.25
p-value of test                       :  7.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   51.81
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:06.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.32
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.06
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5017.29
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:54.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46057
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870057
  j =  1                              :        399907889
  j =  2                              :            46051
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45655
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869655
  j =  1                              :        399908693
  j =  2                              :            45649
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:27.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:18.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:00.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:55.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.83e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.68e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 5.58e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:31.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.020
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:34.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.81
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.41
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.82
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.64
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.65
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.71
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:38.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.44
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.01
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.62
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17654.44
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.51
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.50
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.88
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.98
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.90
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.54
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.50
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.51
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.52
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.49
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.98
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.04
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.52
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.13
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.47
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.13
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.05
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.00
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.26
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.96
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  308.75
p-value of test                       :    0.9981


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.09
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5193.51
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.64
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.10
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.90
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.84
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.89
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.06
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  155.35
p-value of test                       :    0.9916


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.85
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:20.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.47
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:20.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.21e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.07
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.85
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.71
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:05.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10074.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10103.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:41.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4771.43
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:54.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5124.35
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.38
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.46
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11749.59
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12139.70
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.30
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999932594

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.00
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000019051

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:26.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs NP, t = 9            7.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 106856456.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5344
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:56.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:41.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:04.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:54.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:57.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.83
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:11.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:37.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.07
p-value of test                       :  1.0e-2

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.35
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.35
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.37
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7189.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.48
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:03.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.42
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.59
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:34.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5238.64
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:58.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45778
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869778
  j =  1                              :        399908448
  j =  2                              :            45770
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45741
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869741
  j =  1                              :        399908521
  j =  2                              :            45735
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:27.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-3
p-value of test                       :    0.9988

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:18.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 2.81e-3
p-value of test                       :    0.9970

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:55.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.70e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 3.52e-4
p-value of test                       :  7.0e-3

Anderson-Darling statistic = A2       :    5.25
p-value of test                       :  2.2e-3

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.080
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.20
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.00
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:48.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  101.46
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.88
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.40
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.53
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.01
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:38.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.83
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.07
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.56
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17610.52
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.64
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.26
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.89
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.64
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.43
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.51
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.38
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.73
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.09
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.39
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.45
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.06
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.11
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.10
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.45
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.02
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.36
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.35
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.81
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.19
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.43
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.53
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.12
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.51
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.44
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.47
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.79
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.66
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.84
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.78
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.34
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:22.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.13
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -1.22
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:19.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -2.04
p-value of test                       :    0.98

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.53
p-value of test                       :    0.9942

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 2.48e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.90e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 8.82e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.64
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.75
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.70
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:04.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.00
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.35
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10112.76
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:40.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.04e-3
p-value of test                       :    0.9902

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5072.39
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.44
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.88
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3977.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11892.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11785.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   86.51
p-value of test                       :  3.3e-3


-----------------------------------------------
Total number of bits:  8000228817

Normal statistic for number of bits   :    1.81
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.95
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999982592

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.32

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:28.64

 All tests were passed




Server wird beendet - Lösche Semaphor 107741192.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5437
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:59.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:43.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:44.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:11.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:09.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:13.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:11.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:40.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.70
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.04
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.44
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.48
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.59
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:08.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6957.24
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:58.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.93
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.84
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.02
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:40.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4871.57
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:54.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46200
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870200
  j =  1                              :        399907604
  j =  2                              :            46192
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46144
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870144
  j =  1                              :        399907715
  j =  2                              :            46138
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:30.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:21.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:54.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:10.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  5.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 3.91e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.43e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:25.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.74
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.62
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.66
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.22
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:53.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.61
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.34
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.74e-3
p-value of test                       :    0.9906

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.61
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17510.42
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.43
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.56
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.58
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.90
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.53
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.75
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.16
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.14
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.18
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.15
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.13
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.92
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.64
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.74
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.40
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.83
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.79
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.66
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.73
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.06
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.75
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.20
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.33
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.96
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.19
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.29
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.07
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.95
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.96
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.22
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:20.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.76
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    1.26
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:21.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.22
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.53
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.46
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:15.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.10
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:05.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-3
p-value of test                       :    0.9981

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10239.24
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10053.59
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.76
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:04:35.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.58
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:51.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5022.81
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.31
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.87
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.13
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:34.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11814.47
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:35.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.77
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999976655

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:14.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.60
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000166201

Normal statistic for number of bits   :    1.31
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 5.67e-3
p-value of test                       :    0.9940

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :  -0.078
p-value of test                       :    0.53

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:16.81

 All tests were passed




Server wird beendet - Lösche Semaphor 108724232.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1574
p-value of test                       :  1.6e-8    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334694
  j =  1                              :        599996852
  j =  2                              :             1574
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:51.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:39.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:04.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:54.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:00.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.04
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    2.01
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:12.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:42.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.24
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.08
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.81
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.82
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.41
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.50
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.00
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  262.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.32
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.28
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6998.96
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.52
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.97
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:03.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.51
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.81
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5025.69
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:07.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45791
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869791
  j =  1                              :        399908419
  j =  2                              :            45789
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46056
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870056
  j =  1                              :        399907888
  j =  2                              :            46056
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:26.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:18.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:54.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:33.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.63e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 9.42e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.87e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.87
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.92
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.23
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.55
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.11
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.66
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.13
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.94
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.13
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.32
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17257.79
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.72
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.34
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.07
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.28
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.26
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.68
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.74
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.06
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.87
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.72
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.36
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.59
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.60
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.62
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.44
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.90
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.57
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.11
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.86
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.01
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.86
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.05
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.67
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.01
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.51
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.17
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.75
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5103.97
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.23
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.73
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.14
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    1.44
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:21.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.99
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:23.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.22e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 8.55e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.39e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.75
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.62
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:07.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10122.16
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9933.29
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:42.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.49
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5056.31
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.86
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.24
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12061.42
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11790.19
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.67
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999974585

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.41
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999987335

Normal statistic for number of bits   :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    2.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:18.02
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           1.6e-8
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 110166024.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5546
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:53.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4209
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:04.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:03.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:54.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:00.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.42
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.99
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:13.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.98
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    2.03
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:40.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.36
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.92
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    4.65
p-value of test                       :    0.9993    *****

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.65
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.61
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.14
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:00.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6985.34
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.55
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:04.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.48
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.60
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:29.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4911.44
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:14.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908201
  j =  2                              :            45895
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46188
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870188
  j =  1                              :        399907628
  j =  2                              :            46180
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  8.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:27.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:19.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:01.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:33.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:34.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.79
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.66
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:48.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.48
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.03
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:40.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.14
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.88
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.66
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17136.78
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:52.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.49
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.02
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.43
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.12
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.17
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.57
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.68
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.42
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.27
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.69
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.93
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.05
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.06
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.11
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.77
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.26
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.40
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.11
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.84
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.51
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  431.80
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.14
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.42
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.29
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.91
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.76
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.44
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.95
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    1.79
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.31
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:24.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.25e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.89e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 9.88e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.27
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.30
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.05
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.28
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9883.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10156.60
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:42.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.17
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.18
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3969.84
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4051.84
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11921.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12005.31
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.34
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000050914

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.44
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000100600

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:45.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 29  SimpPoker, r = 25               0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 111116296.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5412
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:54.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4208
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:03.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:55.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:00.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    2.28
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.78
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:13.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:41.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.81
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.30
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.27
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.64
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.15
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:45.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.50
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:01.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7089.27
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:41.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.45
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:01.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.67
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.03
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4827.83
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:10.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45948
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869948
  j =  1                              :        399908107
  j =  2                              :            45942
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45758
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869758
  j =  1                              :        399908485
  j =  2                              :            45756
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:28.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:17.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  6.1e-3

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  1.1e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    8.01
p-value of test                       :  1.2e-4    *****


-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:33.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 8.02e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.50
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:47.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.13
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.20
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.57
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.09
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.89
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17632.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.80
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.14
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.26
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.99
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.74
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.54
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.35
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.95
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.26
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.46
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.75
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.70
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.53
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.56
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.44
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.15
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.12
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.30
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.71
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.50
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.45
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.99
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.84
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.39
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5095.38
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.95
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.15
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.45
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   0.097
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.77
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:23.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.87e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.61e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 8.09e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.91
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.40
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.00
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:06.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.93
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10015.61
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.29
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5048.21
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.04
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.32
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11871.49
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11732.19
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.51
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999972107

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.55
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000024916

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.13
p-value of test                       :    0.98

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.44
p-value of test                       :    0.08

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:18.32
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 49  MaxOft AD, t = 32               1.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 112066568.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5355
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:54.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7528
p-value of test                       :  7.4e-3


-----------------------------------------------
CPU time used                    :  00:03:05.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:03.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:53.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:00.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     959
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:13.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:41.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.41
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.97
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.20
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.13
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.37
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.26
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.28
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7025.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.38
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.17
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:03.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.54
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:33.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5140.14
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:59.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45738
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869738
  j =  1                              :        399908528
  j =  2                              :            45730
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46129
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870129
  j =  1                              :        399907752
  j =  2                              :            46109
  j =  3                              :               10
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:24.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:16.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.30
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:44.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.96e-4
p-value of test                       :    0.9994    *****

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 7.13e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 4.21e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.84
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.076
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:34.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.08
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:48.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.62
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:48.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.38
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.92
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.69
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.20
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17626.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.90
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.61
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.50
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.99
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.16
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.43
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.69
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.79
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.56
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.23
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.51
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.38
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.30
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.67
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.67
p-value of test                       :    0.9939


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.15
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.45
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.57
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.08
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.32
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.87
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.33
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.86
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.93
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.03
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.80
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.36
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.67
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.01
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:23.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.61
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    1.52
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:22.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.11e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 4.93e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.87
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.99
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.85
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:05.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.07
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:07.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.15
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9851.62
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:38.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.34
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3924.93
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11754.07
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.09
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.47
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999935525

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.17
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000040105

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:50.87

 All tests were passed




Server wird beendet - Lösche Semaphor 113049608.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5472
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:55.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:41.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:57.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7118
p-value of test                       :    0.9905


-----------------------------------------------
CPU time used                    :  00:03:03.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:55.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:00.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    3.53
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.61
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:14.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:41.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.54
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.82
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.69
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.47
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.79
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.76
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:01.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7004.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.04
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.93
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:01.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.86
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:35.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4941.80
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:06.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46161
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870161
  j =  1                              :        399907680
  j =  2                              :            46157
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45949
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869949
  j =  1                              :        399908106
  j =  2                              :            45941
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:26.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9914


-----------------------------------------------
CPU time used                    :  00:02:17.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 2.87e-3
p-value of test                       :    0.9970

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  9.6e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:54.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.29e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.57e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:36.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.96
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.96
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.87
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.75
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.34
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.56
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.37
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.93
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17468.44
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.34
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.84
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.87
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.68
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.45
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.11
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.28
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.32
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.11
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.70
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  432.58
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  101.53
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.71
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.79
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.56
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.12
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.83
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.39
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.42
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.96
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.81
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.03
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.91
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.12
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4895.55
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.69
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.82
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.36
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -1.46
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.42
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -1.97
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:22.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 6.59e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 2.84e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.18
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.17
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:04.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:05.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9871.15
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10196.00
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:38.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4676.93
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:47.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.13
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4249.95
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3977.08
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11928.48
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11691.33
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.60
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999944444

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.66
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999918056

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:32.64

 All tests were passed




Server wird beendet - Lösche Semaphor 114032648.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5309
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:55.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:41.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4225
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:05.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:04.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:55.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:00.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9932

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:12.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:43.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.59
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.87
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.24
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.84
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.90
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.77
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.15
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.71
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7032.99
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.93
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:05.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.32
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.80
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:33.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5127.80
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:11.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45934
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869934
  j =  1                              :        399908135
  j =  2                              :            45928
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45654
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869654
  j =  1                              :        399908698
  j =  2                              :            45642
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-3
p-value of test                       :    0.9989

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:26.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:17.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:53.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.17e-3
p-value of test                       :    0.9931

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 5.52e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.48
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:47.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.54
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.79
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.42
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.52
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   13.53
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.29
p-value of test                       :  6.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   76.39
p-value of test                       :  4.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.13
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.94
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.56
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17174.90
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.49
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.34
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.54
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.17
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.95
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.37
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.17
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.31
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.73
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.69
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.59
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.91
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.07
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.98
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.70
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.14
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.87
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.97
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.65
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.58
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.80
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4813.53
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.82
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.81
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.99
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.41
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.65
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  434.59
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.12
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.85
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:24.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.46
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    1.72
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:24.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 4.98e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.77
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.18
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.85
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.47
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9963.15
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10108.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : -1.86e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:39.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4786.11
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:47.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.22
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.14
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.60
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11994.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.01
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000068842

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.91
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000074734

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:24.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 66  MatrixRank, L=30, r=0           4.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 115081224.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5423
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:57.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:58.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:58.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:05.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:59.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:01.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.59
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:54.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:15.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:44.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.68
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.18
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.29
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.96
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.38
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.17
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:03.61

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6977.23
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:45.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.06
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:02.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.06
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   90.96
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5027.49
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:58.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45913
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869913
  j =  1                              :        399908175
  j =  2                              :            45911
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46143
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870143
  j =  1                              :        399907716
  j =  2                              :            46139
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:24.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:17.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.76e-3
p-value of test                       :    0.9923

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:59.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:54.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:34.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.59e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.06e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:29.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.91
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.03
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.36
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.87
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.04
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.97
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.69
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17417.01
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.76
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.85
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.90
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.08
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.83
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.25
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.57
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.41
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.19
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.40
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.50
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.90
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.46
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.24
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.54
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.38
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.60
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.24
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.98
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.57
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.54
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.15
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.23
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.81
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.57
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.34
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.03
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.58
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.91
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.86
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.64
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:22.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.41
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.59
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.65
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:05.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:07.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10084.05
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.65
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.051
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:48.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5060.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.44
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11685.82
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.04
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999922970

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.96
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000090532

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:52.92

 All tests were passed




Server wird beendet - Lösche Semaphor 116097032.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5461
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:56.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7116
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:58.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:07.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:05.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:55.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9901

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    3.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:14.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:42.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.66
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.10
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.97
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.03
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.70
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.68
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.73
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1441.55
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:04.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7135.81
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:01.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.84
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.50
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:32.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5181.84
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:54.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45636
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869636
  j =  1                              :        399908733
  j =  2                              :            45626
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46417
p-value of test                       :  6.2e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870417
  j =  1                              :        399907169
  j =  2                              :            46411
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:26.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:17.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:44.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:54.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.61e-3
p-value of test                       :    0.9973

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:33.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.37e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.66
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.66
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.19
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.19
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.98
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.18
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.41
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.27e-3
p-value of test                       :    0.9987

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16986.50
p-value of test                       :    0.9916



-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.76
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.60
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.84
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.07
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.69
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.70
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.08
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.36
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.01
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.49
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.75
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.44
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.87
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.08
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.00
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.70
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.36
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.60
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.98
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.99
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.04
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.58
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.71
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.08
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.87
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.56
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.02
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.87
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.53
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.98
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -1.92
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.75
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   0.088
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.49e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.62e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.54
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.71
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.40
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:05.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.25
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:06.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9739.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9910.31
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:41.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4779.99
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.22
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.48
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.56
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12024.45
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.24
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999965921

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.07
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999938549

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.069
p-value of test                       :    0.53

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:40.57

 All tests were passed




Server wird beendet - Lösche Semaphor 117014536.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1250
p-value of test                       :    0.9991    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334370
  j =  1                              :        599997500
  j =  2                              :             1250
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5322
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:53.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:42.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:00.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:07.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:05.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:57.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:02.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:15.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.20
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    5.23
p-value of test                       :  2.2e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     120
p-value of test                       :    0.9934

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:48.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.57
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.50
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.68
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.04
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.90
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  475.62
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:44.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.31
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:00.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7023.60
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:44.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.88
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.62
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:59.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.98
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.96
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4922.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:57.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45579
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869579
  j =  1                              :        399908847
  j =  2                              :            45569
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45737
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869737
  j =  1                              :        399908529
  j =  2                              :            45731
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  8.9e-3

Kolmogorov-Smirnov- statistic = D-    : 2.66e-3
p-value of test                       :    0.9971

Anderson-Darling statistic = A2       :    4.01
p-value of test                       :  8.8e-3


-----------------------------------------------
CPU time used                    :  00:02:25.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:18.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.23e-3
p-value of test                       :    0.9954

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:54.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:34.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.78e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-5
p-value of test                       :    0.9903

Kolmogorov-Smirnov- statistic = D-    : 3.08e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.052
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:33.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  104.38
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.84
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.63
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.24
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.87
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.96
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.89
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.32
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.56
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.29
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17350.93
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.57
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.81
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.79
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.90
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.39
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.41
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.62
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.45
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.84
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.04
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.98
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.55
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.37
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.84
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.89
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.55
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.34
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.92
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.72
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.56
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.68
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.07
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.28
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  254.09
p-value of test                       :  5.8e-3


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.94
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.94
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5195.88
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.45
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.86
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.60
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:20.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.97
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:21.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.43e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.23
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.43
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.26
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:06.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10245.24
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.1e-3

Kolmogorov-Smirnov- statistic = D-    : 2.62e-3
p-value of test                       :    0.9973

Anderson-Darling statistic = A2       :    4.46
p-value of test                       :  5.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9571.75
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:38.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.62
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.37
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3994.81
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.58
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.03
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.84
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999995852

Normal statistic for number of bits   :  -0.033
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.96
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000068389

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:00.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  3  CollisionOver, t = 2            0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 117997576.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1471
p-value of test                       :  2.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334591
  j =  1                              :        599997058
  j =  2                              :             1471
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5291
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:57.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:39.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:59.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:59.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:08.42

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:06.15

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:56.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:01.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.19
p-value of test                       :  7.1e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.04
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    2.98
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     845
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.36
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    2.29
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:13.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:44.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.20
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.60
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.09
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.81
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:44.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:00.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7095.87
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:44.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.06
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.37
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:01.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.07
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.79
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:35.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5048.39
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:53.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45885
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869885
  j =  1                              :        399908236
  j =  2                              :            45873
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46042
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870042
  j =  1                              :        399907918
  j =  2                              :            46038
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:26.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:17.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:46.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:54.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:34.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 2.75e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 7.06e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.66
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:48.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.91
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.44
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.77
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.18
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.75
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9947

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17477.32
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.33
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.93
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.02
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.21
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.21
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.25
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.97
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.78
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.03
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.64
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.89
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.99
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.39
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.93
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.07
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.13
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.39
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.84
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.38
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.72
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.74
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.06
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.55
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.74
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.77
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:34.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.40
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.08
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.21
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.25
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.20
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.71
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    1.59
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:22.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.98
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:22.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.43
p-value of test                       :    0.9925

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.79e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.19
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.74
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:04.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:04.37

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9884.98
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10133.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:42.64

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.08
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:50.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4223.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3960.93
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12046.86
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12066.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.13
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999970277

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.04
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999981545

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.23
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-3
p-value of test                       :    0.9982

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.76
p-value of test                       :    0.04

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:15.35

 All tests were passed




Server wird beendet - Lösche Semaphor 119013384.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.86

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:56.36

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:41.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:08.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:06.30

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:56.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:02.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     952
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.49
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:14.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:42.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.37
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.98
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.19
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.66
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.11
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1504.50
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7079.59
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:42.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   48.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   93.28
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:03:02.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.21
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.64
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4780.43
p-value of test                       :    0.9955


-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:56.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45957
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869957
  j =  1                              :        399908092
  j =  2                              :            45945
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45470
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869470
  j =  1                              :        399909064
  j =  2                              :            45462
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:26.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:18.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:46.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:54.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:34.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.02e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:31.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.44
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.06
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.59
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:48.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.89
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.48
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.9e-3

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.05
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17653.88
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.96
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.60
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.04
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.28
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.47
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.91
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.92
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.39
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.77
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.26
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.31
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.98
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.63
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.84
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.96
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.33
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.27
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.55
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.05
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.19
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5216.12
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.14
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.58
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.07
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.77
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5082.36
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.94
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.06
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.62
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:21.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.22
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:21.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.61e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.32e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.11
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.22
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.90
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:04.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:03.29

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10078.23
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9974.04
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.049
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:39.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5034.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.42
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:50.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.44
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.07
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11520.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.56
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.23
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999968318

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.19
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999979646

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9957

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:42.22

 All tests were passed




Server wird beendet - Lösche Semaphor 120029192.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5386
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:57.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:42.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:00.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:02.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:14.21

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:07.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:13.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    2.93
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     538
p-value of test                       :    0.9946

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:14.38

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    2.03
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:44.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.94
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.54
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.69
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.01
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.68
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:54.26

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1401.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:06.23

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7105.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.31
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:16.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.45
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  155.64
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5009.19
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:57.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46073
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870073
  j =  1                              :        399907858
  j =  2                              :            46065
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45949
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869949
  j =  1                              :        399908106
  j =  2                              :            45941
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:30.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:18.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:05.69

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:37.34

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:40.72

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:41.22

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.76
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.75
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.40
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.36
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:51.31

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.41
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.06
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:40.44

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17627.00
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:52.04

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.86
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.97
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.51
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.81
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.41
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.15
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.77
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.91
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.28
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.35
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.62
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  558.65
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.88
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.93
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.05
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.02
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.79
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.47
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.30
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.13
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.39
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4798.46
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.32
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  151.94
p-value of test                       :    0.9953


-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.88
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.80
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.52
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.52
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.18
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.04
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:20.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.22
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:19.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.36e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 8.59e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.44e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.08
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.01
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.19
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.50
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.77
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9951.17
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:04:25.70

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4768.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:54.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4775.21
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4195.57
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11571.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:35.00

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11559.50
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:33.45

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.02
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999997124

Normal statistic for number of bits   :  -0.023
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.02
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000025816

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n92, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:48.65

 All tests were passed




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